Weighted Morrey and weighted fractional Sobolev–Morrey spaces estimates for a large class of pseudo-differential operators with smooth symbols

Abstract

In this paper, we study the boundedness results for a large class of pseudo-differential operators with smooth symbols on weighted Morrey and Weighted fractional Sobolev-Morrey spaces, respectively.

Weighted Anisotropic Morrey Spaces Estimates for Anisotropic Maximal Operators

“…Thus from this viewpoint, Theorem 4 and Theorem 4 below improve the corresponding results in [3], [4]. In other words, in this paper our goal is to extend results in [3], [4].…”

“…We also refer to [2], [3] for the latest research on the theory of Morrey spaces associated with harmonic analysis. Next, we recall the definition of weighted Lebesgue spaces.…”

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

“…We also refer to [1] for the latest research on the theory of Morrey spaces associated with Harmonic Analysis. In recent years, more and more researches focus on function spaces based on Morrey spaces to fill in some gaps in the theory of Morrey type spaces (see, for example, [9,10,11,12,13,18]). Moreover, these spaces are useful in harmonic analysis and PDEs.…”

Vanishing generalized Morrey spaces and commutators of Marcinkiewicz integrals with rough kernel associated with Schrödinger operator

“…Here, 1 < p < ∞ and 0 < λ < n and the quantity of (1.1) is the (p, λ)-Morrey norm, denoted by f L p,λ . In recent years, more and more researches focus on function spaces based on Morrey spaces to fill in some gaps in the theory of Morrey type spaces (see, for example, [7,8,9,10,11,16]). Moreover, these spaces are proved useful in harmonic analysis and PDEs.…”