Bounded Mean Oscillation Space Research Articles

Global gradient estimates for shear thinning-type Stokes system on the non-smooth domains

In this paper, we present the global $L^q$ estimates for the weak solution of the steady p-Stokes equations describing the motion of the shear-thinning flow under the nonslip boundary condition. Our interest is a non-smooth domain whose boundary can go beyond the Lipschitz category, and the coefficients belong to BMO(Bounded Mean Oscillation) space with sufficiently small BMO semi-norm.

Stability and boundedness of regular solutions for a Sisko flow in an infinite annular porous space

The present article is intended to study the boundedness of solutions for an unsteady non-Newtonian flow, whose strain–stress relationship is provided by the Sisko fluid model. Such kind of flow can appear in different scenarios, but we make it particular to the field of magnetohydrodynamics, as it is a remarkable area of research in its own right. The ideas exposed in this work can be extended, in a similar manner, to a wide range of applications. To make our fluid further general, we use the Darcy’s law to characterize the porous space in which the fluid is flowing. We develop the boundedness criteria provided that the velocity w and the function g=−∂w/∂r satisfy w,g,∂g/∂r,∂2g/∂r2∈L2(0,T;BMO), where BMO means bounded mean oscillation space. For this purpose, we will consider energy estimates in Sobolev spaces and develop the boundedness criteria for the resulting unsteady parabolic nonlinear equation.

Commutators of Hardy-Littlewood operators on p-adic function spaces with variable exponents

Abstract In this article, we obtain some sufficient conditions for the boundedness of commutators of p p -adic Hardy-Littlewood operators with symbols in central bounded mean oscillation space and Lipschitz space on the p p -adic function spaces with variable exponents such as the p p -adic local central Morrey, p p -adic Morrey-Herz, and p p -adic local block spaces with variable exponents.

BMO-space for non-absolute integrable functions

The functions with bounded mean oscillation (BMO) have been shown to be immense interest in several areas of analysis and probability. We introduce BMO-type space BMOHK(Rn) for non-absolute integrable functions. Various properties and completion of BMOHK(Rn) are included. Relations between the classical BMO space and BMOHK(Rn) are investigated.

Dirichlet problem for Schrödinger equation with the boundary value in the BMO space

Let (X, d, μ) be a metric measure space satisfying a Q-doubling condition (Q > 1) and an L2-Poincaré inequality. Let $${\cal L} = {\cal L} + V$$ be a Schrödinger operator on X, where $${\cal L}$$ is a non-negative operator generalized by a Dirichlet form, and V is a non-negative Muckenhoupt weight that satisfies a reverse Hölder condition RHq for some q ⩾ (Q + 1)/2. We show that a solution to $$({\cal L} - \partial _t^2)u = 0$$ on X × ℝ+ satisfies the Carleson condition $$\mathop {{\rm{sub}}}\limits_{B({x_B},{r_B})} {1 \over {\mu (B({x_B},{r_B}))}}\int_0^{{r_B}} {\int_{B({x_B},{r_B})} {{{\left| {t\nabla u(x,t)} \right|}^2}{{d\mu dt} \over t} < \infty } } $$ if and only if u can be represented as the Poisson integral of the Schrödinger operator ℒ with the trace in the BMO (bounded mean oscillation) space associated with ℒ.

Boundedness for the Modified Fractional Integral Operator from Mixed Morrey Spaces to the Bounded Mean Oscillation Space and Lipschitz Spaces

In this paper, we establish the boundedness of the modified fractional integral operator from mixed Morrey spaces to the bounded mean oscillation space and Lipschitz spaces, respectively.

A characterization of via the commutator of Hardy-type operators on mixed Herz spaces

In this paper, we introduce and study the mixed central bounded mean oscillation space , which is a new central version of the bounded mean oscillation spaces BMO. The pre-dual of is proved to be the mixed Herz–Hardy space . Moreover, we also give a characterization of via the boundedness of the commutators of n-dimensional Hardy operator and its dual operator on mixed Herz spaces .

The Boundedness for Commutators of Anisotropic Calderón-Zygmund Operators

Let T be an anisotropic Calderon-Zygmund operator and φ : ℝn × [0, ∞) → [0, ∞) be an anisotropic Musielak-Orlicz function with φ(x, ·) being an Orlicz function and φ(·,t) being a Muckenhoupt A∞ (A) weight. In this paper, our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators. Precisely, when b ∈ BMOw(ℝn, A) (a proper subspace of anisotropic bounded mean oscillation space BMO(ℝn, A)), the commutator [b, T] is bounded from anisotropic weighted Hardy space Hl(ℝn, A) to weighted Lebesgue space Lw1 (ℝn) and when b ∈ BMO(ℝn) (bounded mean oscillation space), the commutator [b, T] is bounded on Musielak-Orlicz space Lφ(ℝn), which are extensions of the isotropic setting.

Iterated Commutators for Multilinear Singular Integral Operators on Morrey Space with Non-Doubling Measures

Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces .Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.

Local solvability for a class of linear operators in Triebel-Lizorkin spaces

We show local solvability in Triebel-Lizorkin spaces for a class of first order linear operators L defined on an open set of Rn+1, n∈N, satisfying the condition (P) of Nirenberg-Treves and whose coefficients are Hölder continuous. Moreover, when n=1, we show local solvability for L, in Lp(R,h1(R)), 1<p≤∞, where F1,20=h1 (local Hardy space), local solvability for L in bmo(R2) where F∞,20=bmo(R2) (local bounded mean oscillation space) and local solvability for L in Lr(R,Fp,qs(R)), 1≤r≤∞, 1<p<q≤∞ and s∈R.

Image Restoration Models Based on Dyadic Hardy Space and Dyadic Bounded Mean Oscillation Space

Texture is widely existed in various images and plays an important role in many area such as medical image diagnosis, remote sensing, etc. However, the image in texture regions is tend to be deteriorated during restoration process. In this paper, we apply the dyadic Hardy space $H_{d}^{1}$ and dyadic Bounded Mean Oscillation (BMO) space in the texture preserving image restoration model. We propose a $H_{d}^{1}$ regularized minimization model to extract texture from noisy data. In this model, $H^{1}_{d}$ norm is taken as regularizer to enforce the prior that the local variance of the noise is below certain level depending on the regularization parameter. We also analyze the mathematical properties of this model which indicate the mechanism of $H^{1}_{d}$ regularizer to control the local variance. For the numerical solution of the model, we transform it into wavelet domain based on the wavelet characterization of dyadic Hardy space and dyadic BMO space, and solve it by the fixed iteration algorithm. Combing the total variation (TV) regularization method and frame based regularization method, a two-layers regularization model is proposed for edge and texture preserving, and then analyzed and solved in the frame of split Bregman method. Finally, we present various numerical results on images to demonstrate the potential of our methods.

The average concentration function of dissolved copper in Hun River, Liaoning province, Northeastern China.

Water samples were collected from Hun River to research the change in the concentration of dissolved copper and its distribution as well as accumulation during the dry season in 2013. The mean concentrations of dissolved copper in Hun River were 0.1057-0.1533mg/l during the dry season. The results indicated that the most severe dissolved copper pollution were associated with the mining area, industrial area, and living area along the Hun River. The results also indicated that controlling the sources of copper pollution effectively reduced the concentration of dissolved copper in Hun River. The concentration function about time and spatial coordinate, average concentration function about time coordinate, average concentration function about spatial coordinate, and bounded mean oscillation space were used to evaluate the extent of copper pollution in Hun River. The error function, quartiles, and curve fitting tool were performed to determine the stations with high concentration of dissolved copper in Hun River. We furthermore obtained the upper and lower bounds of the error between two kinds of bounded mean oscillation spaces to explore the migration of copper pollution in Hun River. The results of the average concentration function and bounded mean oscillation space revealed that the long-term control measures of copper pollution and short-term control measures of copper pollution, the control of copper pollution in large watershed, and the control of copper pollution in small watershed in Hun River should be combined with each other. The strict policy and pollution control strategy should be implemented to ensure that the water of the Hun River meets the natural environment standard for the growth of aquatic life and human.

Equivalence of BMO-type Norms with Applications to the Heat and Stokes Semigroups

We introduce various spaces of functions of bounded mean oscillation (BMO) defined in a domain by taking into account the behavior of functions near the boundary. Then we establish several equivalences of these spaces. Moreover, we compare our space with a BMO space introduced by Miyachi. As an application we prove that the heat and the Stokes semigroup are analytic in such a type of spaces.

Interpolation of noncommutative quasimartingale spaces

Let Lˆp(M) be the space of bounded Lp(M)-quasimartingales. We prove that, with equivalent norms, (Lˆp0(M),Lˆp1(M))θ,p=Lˆp(M), where 1<p0,p1≤∞, 1<θ<1, and 1p=1−θp0+θp1. We also prove that, for 1<p<q<∞, (BMOˆc(M),Hˆpc(M))pq,q=Hˆqc(M) and (BMOˆr(M),Hˆpr(M))pq,q=Hˆqr(M), where Hˆp(M) and BMOˆ(M) are, respectively, the Hardy space and the bounded mean oscillation space of noncommutative quasimartingales.

The boundedness of Hilbert transform in the local Morrey–Lorentz spaces

ABSTRACTIn this paper, we investigate the boundedness of the Hilbert transform H in the local Morrey–Lorentz spaces , , . We prove that the operator H is bounded in under the condition , . In the limiting case , , we prove that the operator H is bounded from the space to the weak local Morrey–Lorentz space . Also we show that for the limiting case ,, the modified Hilbert transform is bounded from the space to the bounded mean oscillation space.

Regular orthogonal basis on Heisenberg group and application to function spaces

In this paper, we construct some compactly supported orthogonal regular wavelet basis on Heisenberg group . Because of the regularity of wavelets, we could use such wavelets to characterize function spaces on , such as bounded mean oscillation space (BMO) space, Hardy space, Besov spaces and Besov–Morrey spaces. Copyright © 2014 John Wiley &amp; Sons, Ltd.

New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications

AbstractIn this paper, we introduce and develop some new function spaces of BMO (bounded mean oscillation) type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type. The new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity, and they generalize the classical BMO space. We show that the John‐Nirenberg inequality holds on these spaces and they interpolate withLpspaces by the complex interpolation method. We then give applications onLp‐boundedness of singular integrals whose kernels do not satisfy the Hörmander condition. © 2005 Wiley Periodicals, Inc.

On p-adic Bounded Functions, II

In this paper, besides the definition of maximal operators over the p-adic number field using the properties of Section 1, we can define p-adic bounded mean oscillation space and obtain its examples. We prove sufficient conditions of boundedness of maximal operators over the p-adic number field.

The central BMO spaces and Littlewood-Paley operators

The authors give a characterization of central bounded mean oscillation space CBMO2(Rγ) in terms of the central Carleson measure. Using this character, the authors establish the CBMO2(Rγ)-boundedness for several classes of general Littlewood-Paley operators.