On 2-Microlocal Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents (Journal of Mathematical Study, 2021)
In this paper, 2-microlocal Herz type Besov and Triebel-Lizorkin spaces withvariable exponents are introduced for the first time. Then, we give characterizations ofthese spaces by so-called Peetre's maximal functions. Further, the atomic and molecular decompositions of these spaces are obtained. Finally, using the characterizations ofthe spaces by local means and molecular decomposition we obtain the wavelet characterizations.
Keywords: 2-microlocal; variable exponent; Herz type spaces; Besov spaces; Triebel-Lizorkin spaces; Peetre's maximal operator.