Weighted Boundedness of Certain Sublinear Operators in Generalized Morrey Spaces on Quasi-Metric Measure Spaces Under the Growth Condition

Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces

In this paper, we obtain bounded criteria on certain weighted Morrey spaces for the commutators generalized by some sublinear integral operators and weighted Lipschitz functions. We also present bounded criteria for commutators generalized by such sublinear integral operators and weighted BMO function on the weighted Morrey spaces. As applications, our results yield the same bounded criteria fo...

Fractional Integral Operators in Generalized Morrey Spaces Defined on Metric Measure Spaces

We derive some necessary and sufficient conditions for the boundedness of fractional integral operators in generalized Morrey spaces defined on metric measure spaces. îâäæñéâ. áŽéðçæùâIJñèæŽ äëéæŽê éâðîæçñè ïæãîùââIJäâ àŽêïŽäôãîñèæ àŽêäëàŽáëâIJñè ûæèŽáñîæ æêðâàîŽèñîæ ëìâîŽðëîæï öâéëïŽäôãîñèëIJæï ŽñùæèâIJâèæ ᎠïŽçéŽîæïæ ìæîëIJâIJæ.

Weighted Anisotropic Product Hardy Spaces and Boundedness of Sublinear Operators

Let A1 and A2 be expansive dilations, respectively, on R n and R. Let ~ A ≡ (A1, A2) and Ap( ~ A) be the class of product Muckenhoupt weights on R × R for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ Ap( ~ A), the authors characterize the weighted Lebesgue space L w (R × R) via the anisotropic Lusin-area function associated with ~ A. When p ∈ (0, 1], w ∈ A∞( ~ A), the authors introduce the weighted anis...

Boundedness of Sublinear Operators on the Homogeneous Herz Spaces

Localized Morrey-Campanato Spaces on Metric Measure Spaces and Applications to Schrödinger Operators

Let X be a space of homogeneous type in the sense of Coifman and Weiss and D a collection of balls in X . The authors introduce the localized atomic Hardy space H q D (X ) with p ∈ (0, 1] and q ∈ [1,∞] ∩ (p,∞], the localized Morrey-Campanato space E p D (X ) and the localized Morrey-Campanato-BLO space Ẽ p D (X ) with α ∈ R and p ∈ (0,∞) and establish their basic properties including H q D (X )...