Multi-sublinear Operators Research Articles

Multi-sublinear operators and their commutators on product generalized mixed Morrey spaces

In this paper, we study the boundedness for a large class of multi-sublinear operators T m generated by multilinear Calderón-Zygmund operators and their commutators T m , i b ( i = 1 , … , m ) on the product generalized mixed Morrey spaces M q 1 → φ 1 ( R n ) × ⋯ × M q m → φ m ( R n ) . We find the sufficient conditions on ( φ 1 , … , φ m , φ ) which ensure the boundedness of the operator T m from M q 1 → φ 1 ( R n ) × ⋯ × M q m → φ m ( R n ) to M q → φ ( R n ) . Moreover, the sufficient conditions for the boundeness of T m , i b from M q 1 → φ 1 ( R n ) × ⋯ × M q m → φ m ( R n ) to M q → φ ( R n ) are also studied. As applications, we obtain the boundedness for the multi-sublinear maximal operator, the multilinear Calderón-Zygmund operator and their commutators on product generalzied mixed Morrey spaces.

Boundedness Criterion for Multi-sublinear Operators and Their Commutators Generated by Multilinear Fractional Integral Operator on Product Generalized Mixed Morrey Spaces

Boundedness Criterion for Multi-sublinear Operators and Their Commutators Generated by Multilinear Fractional Integral Operator on Product Generalized Mixed Morrey Spaces

Some estimates of multi-sublinear operators and commutators on mixed $$\lambda $$-central Morrey spaces

Some estimates of multi-sublinear operators and commutators on mixed $$\lambda $$-central Morrey spaces

Product generalized local Morrey spaces and commutators of multi-sublinear operators generated by multilinear Calderon-Zygmund operators and local Campanato functions

The aim of this paper is to get the boundedness of the commutators of multi-sublinear operators generated by local campanato functions and multilinear Calder?n-Zygmund operators on the product generalized local Morrey spaces.

Multi-sublinear operators generated by multilinear Calderon-Zygmund ´ operators on product generalized Morrey spaces

Multi-sublinear operators generated by multilinear Calderon-Zygmund ´ operators on product generalized Morrey spaces

A Sparse Estimate for Multisublinear Forms Involving Vector-valued Maximal Functions

We prove a sparse bound for the m -sublinear form associated to vector-valued maximal functions of Fefferman-Stein type. As a consequence, we show that the sparse bounds of multisublinear operators are preserved via l r -valued extension. This observation is in turn used to deduce vector-valued, multilinear weighted norm inequalities for multisublinear operators obeying sparse bounds, which are out of reach for the extrapolation theory developed by Cruz-Uribe and Martell in Limited range multilinear extrapolation with applications to the bilinear Hilbert transform , preprint arXiv:1704.06833 (2017). As an example, vector-valued multilinear weighted inequalities for bilinear Hilbert transforms are deduced from the scalar sparse domination theorem of Domination of multilinear singular integrals by positive sparse forms , preprint arXiv:1603.05317.

The multisublinear maximal type operators in Banach function lattices

The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces.

SOME MULTI-SUBLINEAR OPERATORS ON GENERALIZED MORREY SPACES WITH NON-DOUBLING MEASURES

In this paper the boundedness for a large class of multi-sublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calder<TEX>$\acute{o}$</TEX>n-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

Multilinear extrapolation and applications to the bilinear Hilbert transform

We present two extrapolation methods for multi-sublinear operators that allow us to derive estimates for general functions from the corresponding estimates on characteristic functions. Of these methods, the first is applicable to general multi-sublinear operators while the second requires working with the so-called ( ε , δ ) -atomic operators. Among the applications, we discuss some new endpoint estimates for the bilinear Hilbert transform.

λ-central BMO estimates for commutators of singular integral operators with rough kernels

The authors establish λ-central BMO estimates for commutators of singular integral operators with rough kernels on central Morrey spaces. Moreover, the boundedness of a class of multisublinear operators on the product of central Morrey spaces is discussed. As its special cases, the corresponding results of multilinear Calderon-Zygmund operators and multilinear fractional integral operators can be deduced, respectively.

Multilinear Calderón-Zygmund operator on Morrey type spaces

In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderon-Zygmund operator can be obtained.