Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz–Morrey spaces with variable exponents. Next we introduce weighted grand Herz–Morrey–Triebel–Lizorkin spaces with variable exponents and provide their equivalent quasi-norms via maximal functions.

The Weighted Grand Herz–Morrey–Lizorkin–Triebel Spaces with Variable Exponents

Abstract In this paper, our goal is to further introduce the weighted grand variableHerz-Morrey spaces and establish the boundedness of fractional sublinear operatorsand their multilinear commutators on the weighted grand variable Herz-Morrey s-paces. The results are still new even in the unweighted setting, which generalizes theprevious work of Wang et al. [17] and Zhang et al. [19]. 

Boundedness of fractional sublinear operators on weightedgrand Herz-Morrey spaces with Variable Exponents

Grand weighted variable Herz-Morrey spaces estimate for some operators

Abstract In this article, we obtain some sufficient conditions for the boundedness of commutators of p p -adic Hardy-Littlewood operators with symbols in central bounded mean oscillation space and Lipschitz space on the p p -adic function spaces with variable exponents such as the p p -adic local central Morrey, p p -adic Morrey-Herz, and p p -adic local block spaces with variable exponents.

/pdf/commutators-of-hardy-littlewood-operators-on-p-adic-function-27jbdi2o.pdf

Commutators of Hardy-Littlewood operators on p-adic function spaces with variable exponents

<abstract>In this paper, we introduce weighted grand Herz-Morrey type spaces and prove the boundedness of sublinear operators and their multilinear commutators on these spaces. The results are still new even in the unweighted setting.</abstract>

Boundedness of sublinear operators on weighted grand Herz-Morrey spaces

/pdf/boundedness-of-vector-valued-sublinear-operators-on-weighted-3nht67f329.pdf

Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents

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Boundedness of vector-valued sublinear operators on weighted Herz-Morrey spaces with variable exponents