Artículo
Characterizations of the boundedness of generalized fractional maximal functions and related operators in Orlicz spaces
Fecha de publicación:
01/2017
Editorial:
Wiley VCH Verlag
Revista:
Mathematische Nachrichten
ISSN:
0025-584X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Given 0 <α< n and a Young function η, we consider the generalized fractional maximal operator Mα,η defined by Mα,η f (x) = sup Bx |B| α/n || f ||η,B, where the supremum is taken over every ball B contained in Rn . In this article, we give necessary and sufficient Dini type conditions on the functions A, B and η such that Mα,η is bounded from the Orlicz space LA(Rn ) into the Orlicz space LB(Rn ). We also present a version of this result for open subsets of Rn with finite measure. Both results generalize those contained in [6] and [14] when η(t) = t, respectively. As a consequence, we obtain a characterization of the functions involved in the boundedness of the higher order commutators of the fractional integral operator with BMO symbols. Moreover, we give sufficient conditions that guarantee the continuity in Orlicz spaces of a large class of fractional integral operators of convolution type with less regular kernels and their commutators, which are controlled by Mα,η.
Palabras clave:
Orlicz Spaces
,
Fractional Maximal Functions
,
Fractional Integrals
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Articulos(IMAL)
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Citación
Dalmasso, Estefanía Dafne; Pradolini, Gladis Guadalupe; Characterizations of the boundedness of generalized fractional maximal functions and related operators in Orlicz spaces; Wiley VCH Verlag; Mathematische Nachrichten; 290; 1; 1-2017; 19-36
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