Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Lu, Yan   ; Zhu, Yue Ping

Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 969-987

Abstract (VO)

We introduce a new type of variable exponent function spaces $M\dot K^{\alpha (\cdot ),\lambda }_{q,p(\cdot )}(\mathbb R^n)$ of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents $\alpha $ and $p$ are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators of BMO function on these Morrey-Herz type spaces by applying the properties of variable exponent and BMO norms.

Détail

DOI : 10.1007/s10587-014-0147-0

Classification : 42B25, 42B35
Keywords: Morrey-Herz space; variable exponent; sublinear operator; commutator

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