Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent. (September 2020) - Izuki, Mitsuo; Nogayama, Toru; Noi, Takahiro; Sawano, Yoshihiro
Abstract: Our aim in this paper is to characterize local Muckenhoupt weighted Lebesgue spaces with variable exponent by compactly supported smooth wavelets. We also investigate necessary and sufficient conditions for the corresponding modular inequalities to hold. One big achievement is that the weights with exponential growth can be handled in the framework of variable exponents.