Morrey-type Banach spaces, maximal operator and Fourier multipliers

V. S. Guliev^a, Zhijian Wu^b, Ying Xiao<sup>c

a</sup> Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
^b Department of Mathematics, University of Alabama at Tuscaloosa
^c China University of Political Science and Law

Abstract: Let $({\mathcal F},\norm{\cdot}_{{\mathcal F}})$ be a Banach space of complex-valued measurable functions on $\Rnn$. In this paper, we consider the Morrey-type Banach space ${\mathcal M}_ {\mathcal F}(p,\lambda)$ as well as its weak type ${\mathcal M}_{\mathcal F}^*(1,\lambda)$. We develop the theory of maximal operator and Fourier multipliers on these spaces.

MSC: Primary 42B25; Secondary 31C15

Language: English