Homogeneous fractional integral operators on Lebesgue and Morrey spaces, Hardy--Littlewood--Sobolev and Olsen-type inequalities

2022/12/26 by Yang, Kaikai, Wang, Hua · 1 citation
#42B20 #42B25 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2212.14774

Abstract

Let T_Ω,α be the homogeneous fractional integral operator defined as T_Ω,αf(x):=∫_{\mathbb Rⁿ}\fracΩ(x-y)|x-y|^n-αf(y) dy, and the related fractional maximal operator M_Ω,α is given by \beginequation* M_Ω,αf(x):=sup_r>0\frac1|B(x,r)|^1-α/n∫_|x-y|

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• Homogeneous fractional integral operators on weighted Lebesgue, Morrey and Campanato spaces

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