SUBLINEAR OPERATORS WITH ROUGH KERNEL GENERATED BY FRACTIONAL INTEGRALS AND COMMUTATORS ON GENERALIZED VANISHING LOCAL MORREY SPACES

SUBLINEAR OPERATORS WITH ROUGH KERNEL GENERATED BY FRACTIONAL INTEGRALS AND COMMUTATORS ON GENERALIZED VANISHING LOCAL MORREY SPACES

F. Gürbüz

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Abstract

In this work, we consider the norm inequalities for sublinear operators with rough kernel generated by fractional integrals and commutators on generalized vanishing local Morrey spaces including their weak versions under generic size conditions which are satised by most of the operators in harmonic analysis, respectively.

Keywords

Sublinear operator, Fractional integral operator, Rough kernel, Generalized vanishing local Morrey space, Commutator, Local Campanato space