Geodesic
Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 969-987 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10587-014-0147-0
Classification : 42B25, 42B35
Keywords: Morrey-Herz space; variable exponent; sublinear operator; commutator 
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     title = {Boundedness of some sublinear operators and commutators on {Morrey-Herz} spaces with variable exponents},
     journal = {Czechoslovak Mathematical Journal},
     pages = {969--987},
     year = {2014},
     volume = {64},
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Lu, Yan; Zhu, Yue Ping. Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 969-987. doi: 10.1007/s10587-014-0147-0

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