Radial Weight Research Articles

Atomic Decomposition and Carleson Measures for Weighted Mixed Norm Spaces

The purpose of this paper is to establish an atomic decomposition for functions in the weighted mixed norm space $$A^{p,q}_\omega $$ induced by a radial weight $$\omega $$ in the unit disc admitting a two-sided doubling condition. The obtained decomposition is further applied to characterize Carleson measures for $$A^{p,q}_\omega $$ , and bounded differentiation operators $$D^{(n)}(f)=f^{(n)}$$ acting from $$A^{p,q}_\omega $$ to $$L^s_\mu $$ , induced by a positive Borel measure $$\mu $$ , on the full range of parameters $$0<p,q,s<\infty $$ .

Embeddings of Weighted Generalized Morrey Spaces Into Lebesgue Spaces on Fractal Sets

Abstract We study embeddings of weighted local and consequently global generalized Morrey spaces defined on a quasi-metric measure set (X, d, μ) of general nature which may be unbounded, into Lebesgue spaces Ls (X), 1 ≤ s ≤ p &lt; ∞. The main motivation for obtaining such an embedding is to have an embedding of non-separable Morrey space into a separable space. In the general setting of quasi-metric measure spaces and arbitrary weights we give a sufficient condition for such an embedding. In the case of radial weights related to the center of local Morrey space, we obtain an effective sufficient condition in terms of (fractional in general) upper Ahlfors dimensions of the set X. In the case of radial weights we also obtain necessary conditions for such embeddings of local and global Morrey spaces, with the use of (fractional in general) lower and upper Ahlfors dimensions. In the case of power-logarithmic-type weights we obtain a criterion for such embeddings when these dimensions coincide.

GAMA+KiDS: Alignment of galaxies in galaxy groups and its dependence on galaxy scale

Intrinsic galaxy alignments are a source of bias for weak lensing measurements as well as a tool for understanding galaxy formation and evolution. In this work, we measure the alignment of shapes of satellite galaxies, in galaxy groups, with respect to the brightest group galaxy (BGG), as well as alignments of the BGG shape with the satellite positions, using the highly complete Galaxy And Mass Assembly (GAMA) spectroscopic survey and deep imaging from the Kilo Degree Survey. We control systematic errors with dedicated image simulations and measure accurate shapes using the DEIMOS shape measurement method. We find a significant satellite radial alignment signal, which vanishes at large separations from the BGG. We do not identify any strong trends of the signal with galaxy absolute magnitude or group mass. The alignment signal is dominated by red satellites. We also find that the outer regions of galaxies are aligned more strongly than their inner regions, by varying the radial weight employed during the shape measurement process. This behaviour is evident for both red and blue satellites. BGGs are also found to be aligned with satellite positions, with this alignment being stronger when considering the innermost satellites, using red BGGs and the shape of the outer region of the BGG. Lastly, we measure the global intrinsic alignment signal in the GAMA sample for two different radial weight functions and find no significant difference.

A weighted Trudinger-Moser type inequality and its applications to quasilinear elliptic problems with critical growth in the whole Euclidean space

We establish a version of the Trudinger-Moser inequality involving unbounded or decaying radial weights in weighted Sobolev spaces. In the light of this inequality and using a minimax procedure we also study existence of solutions for a class of quasilinear elliptic problems involving exponential critical growth.

Effect of NaCl on the development of the oil palm vascular wilt fungus, Fusarium oxysporum f. sp. elaeidis.

Oil palm Elaeis guineensis Jacq. (Arecaceae) is one of the cash crops that mainly contributes to the gross domestic production of growing countries. This crop is grown worldwide throughout the humid intertropical belt. Its production in Africa is mainly threatened by the telluric fungus Fusarium oxysporum f. sp. elaeidis, causal agent of the oil palm vascular wilt. It has been reported that some environmental factors, such as soil and air salinity, may determine the survival, development and severity of phytopathogenic agents including Fusarium. The purpose of this study was to evaluate the effect of NaCl on growth, reproduction and pathogenic traits of this fungus by measuring mycelium daily growth, mycelium dry weight, sporulation rate, germination rate and number of infectious spores under four NaCl concentrations (0 g.L-1, 2.5 g.L-1, 5 g.L-1 ,10 g.L-1) of culture medium (MM solid medium and Armstrong liquid medium). The results indicated that NaCl reduced the radial daily growth and mycelium dry weight. In addition, the NaCl reduced significantly the sporulation rate and number of infectious spores while increasing the germination rate. Overall, these results indicated the negative NaCl effect on the development and the fitness of this pathogenic fungus. Thus, NaCl inputs appeared to be a potential solution for managing Fusarium oxysporum f. sp. elaeidis in the field, if a good balance between a decrease of disease incidence and yield loss is reached.

Weighted mixed‐norm inequalities through extrapolation

AbstractWe prove that operators satistying weighted inequalities with radial weights are bounded in mixed‐norm spaces of radial‐angular type, even with a weight in the radial part. This is achieved by using the usual extrapolation methods, adapted to the radial setting. All the versions of the extrapolation theorem can be adapted to this setting, and in particular we get results in variable Lebesgue spaces and also for multilinear operators. Furthermore, quantitative estimates are obtained with this approach, but their sharpness remains an open question.

Rapid Parametric Human Modeling in 3D Garment Simulation

Abstract To realize 3D garment simulation online and show the wearing effect of different body types, a method for rapid parametric human modeling is proposed in this article. The parameterization consists of two phases. In the first phase, the characteristic parameters of the sample model are extracted according to the different types of feature information. In the second phase, the deformation is realized by combining the axial deformation method and the radial weight. Thus, according to contrasts between the input measurement and the sample sizes, parametric human modeling is realized by deformation of the sample model. In the deformation stage, the axis curve is simplified to the straight-line segment in the axis deformation method, reducing the calculation. Comparative analysis and the results of experiments demonstrate that the better performance can be achieved at a higher speed, and this method realizes real-time parametric human modeling.

Adaptive Sampling for Sound Propagation.

Precomputed sound propagation samples acoustics at discrete scene probe positions to support dynamic listener locations. An offline 3D numerical simulation is performed at each probe and the resulting field is encoded for runtime rendering with dynamic sources. Prior work place probes on a uniform grid, requiring high density to resolve narrow spaces. Our adaptive sampling approach varies probe density based on a novel "local diameter" measure of the space surrounding a given point, evaluated by stochastically tracing paths in the scene. We apply this measure to layout probes so as to smoothly adapt resolution and eliminate undersampling in corners, narrow corridors and stairways, while coarsening appropriately in more open areas. Coupled with a new runtime interpolator based on radial weights over geodesic paths, we achieve smooth acoustic effects that respect scene boundaries as both the source or listener move, unlike existing visibility-based solutions. We consistently demonstrate quality improvement over prior work at fixed cost.

Zero sequences, factorization and sampling measures for weighted Bergman spaces

The zero sets of the Bergman space A^p_omega induced by either a radial weight omega admitting a certain doubling property or a non-radial Bekollé-Bonami type weight are characterized in the spirit of Luecking’s results from 1996. Accurate results obtained en route to this characterization are used to generalize Horowitz’s factorization result from 1977 for functions in A^p_omega . The utility of the obtained factorization is illustrated by applications to integration and composition operators as well as to small Hankel operator induced by a conjugate analytic symbol. Dominating sets and sampling measures for the weighted Bergman space A^p_omega induced by a doubling weight are also studied. Several open problems related to the scheme of the paper are posed.

Univalent symbols of Volterra operators on growth spaces

Let w and v be arbitrary radial weights on the unit disk \({\mathbb {D}}\). We characterize those univalent symbols \(g\in Hol({\mathbb {D}})\) for which the Volterra operator \(T_g\) maps boundedly the growth space \({\mathcal {A}}^w({\mathbb {D}})\) into \({\mathcal {A}}^v({\mathbb {D}})\).

Translation matrix elements for spherical Gauss–Laguerre basis functions

Spherical Gauss–Laguerre (SGL) basis functions, i.e., normalized functions of the type $$L_{n-l-1}^{(l + 1/2)}(r^2) r^{l} Y_{lm}(\vartheta ,\varphi ), |m| \le l < n \in {\mathbb {N}}$$, constitute an orthonormal polynomial basis of the space $$L^{2}$$ on $${\mathbb {R}}^{3}$$ with radial Gaussian weight $$\exp (-r^{2})$$. We have recently described reliable fast Fourier transforms for the SGL basis functions. The main application of the SGL basis functions and our fast algorithms is in solving certain three-dimensional rigid matching problems, where the center is prioritized over the periphery. For this purpose, so-called SGL translation matrix elements are required, which describe the spectral behavior of the SGL basis functions under translations. In this paper, we derive a closed-form expression of these translation matrix elements, allowing for a direct computation of these quantities in practice.

Hyponormality on general Bergman spaces

A bounded operator T on a Hilbert space is hyponormal if T*T-TT* is positive. We give a necessary condition for the hyponormality of Toeplitz operators on weighted Bergman spaces, for a certain class of radial weights, when the symbol is of the form f+g?, where both functions are analytic and bounded on the unit disk. We give a sufficient condition when f is a monomial.

General weighted Hardy-type inequalities related to Greiner operators

In this article, we present a general method that can be used to deduce weighted Hardy-type inequalities from a particular non-linear partial differential inequality in a relatively simple and unified way on the sub-Riemannian manifold $\mathbb {R}^{2n+1}=\mathbb {R}^{n}\times \mathbb {R}^{n}\times \mathbb {R}$, defined by the Greiner vector fields \[X_{j}=\frac {\partial }{\partial x_{j}}+2ky_{j} \vert z\vert ^{2k-2}\frac {\partial }{\partial l},\] \[Y_{j}=\frac {\partial }{\partial y_{j}}-2kx_{j}|z|^{2k-2}\frac {\partial }{\partial l},\] $j=1,\ldots ,n$, where $z=x+iy\in \mathbb {C}^{n},$ $l\in \mathbb {R}$, $k\geq 1$. Our method allows us to improve, extend, and unify many previously obtained sharp weighted Hardy-type inequalities as well as to yield new ones. These cases are illustrated by giving many concrete examples, including radial, logarithmic, hyperbolic and non-radial weights. Furthermore, we introduce a new technique for constructing two-weight $L^{p}$ Hardy-type inequalities with remainder terms on smooth bounded domains $\Omega $ in $\mathbb {R}^{2n+1}$. We also give several applications leading to various weighted Hardy inequalities with remainder terms.

Integration and Differentiation in Hardy Growth Spaces

We study the integration operator between the growth spaces $$H_w^\infty $$ and $$H_u^\infty $$ on the complex plane with arbitrary radial weights w and u. Also, we investigate the differentiation operator on the Hardy growth spaces $$H_w^p$$ , $$0<p<\infty $$ , defined on the unit disk or on the complex plane. As in the case $$p=\infty $$ , the log-convex weights w play a special role in the problems under consideration.

On the structure of radial solutions for some quasilinear elliptic equations

In this paper we study entire radial solutions for the quasilinear $p$-Laplace equation $\Delta_p u + k(x) f(u) = 0$ where $k$ is a radial positive weight and the nonlinearity behaves e.g. as $f(u)=u|u|^{q-2}-u|u|^{Q-2}$ with $q<Q$. In particular we focus our attention on solutions (positive and sign changing) which are infinitesimal at infinity, thus providing an extension of a previous result by Tang (2001).

A Note on Hardy Inequalities on Homogeneous Groups

We provide the necessary and sufficient characterizations on a pair of positive radial functions so that the two-weight Hardy inequalities hold true on homogeneous groups, one of most general subclasses of nilpotent Lie groups. We also present a simple condition on a couple of positive radial weight functions for the Lp −Hardy type inequalities to be valid.

Distance Formulas on Weighted Banach Spaces of Analytic Functions

Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function $$f_0$$ in the Banach space $$H_v^\infty $$ of all analytic functions f such that v|f| is bounded, the distance of $$f_0$$ to the subspace $$H_v^0$$ of $$H_v^\infty $$ of all the functions g such that v|g| vanishes at infinity is attained at a function $$g_0 \in H_v^0$$ . Moreover a simple, direct proof of the formula of the distance of f to $$H_v^0$$ due to Perfekt is presented. As a consequence the corresponding results for weighted Bloch spaces are obtained.

Solid hulls and cores of weighted $$H^\infty $$ H ∞ -spaces

We determine the solid hull and solid core of weighted Banach spaces $$H_v^\infty $$ of analytic functions functions f such that v|f| is bounded, both in the case of the holomorphic functions on the disc and on the whole complex plane, for a very general class of radial weights v. Precise results are presented for concrete weights on the disc that could not be treated before. It is also shown that if $$H_v^\infty $$ is solid, then the monomials are an (unconditional) basis of the closure of the polynomials in $$H_v^\infty $$ . As a consequence $$H_v^\infty $$ does not coincide with its solid hull and core in the case of the disc. An example shows that this does not hold for weighted spaces of entire functions.

Big Hankel Operators on Vector-Valued Fock Spaces in mathbb {C}^d

We study big Hankel operators acting on vector-valued Fock spaces with radial weights in mathbb {C}^d. We provide complete characterizations for the boundedness, compactness and Schatten class membership of such operators.

Equivalent Bergman Spaces with Inequivalent Weights

We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic functions. Additionally, a family of radial weights in $$L^1(\mathbb {C})$$ whose associated Bergman kernels that have infinitely many zeroes is exhibited.