Abstract
In this paper we study the multilinear fractional integral operators, the multilinear Calderon-Zygmund operators and the multi-sublinear maximal operators defined on the quasi-metric space with non-doubling measure. We obtain the boundedness of these operators on the generalized Morrey spaces over the quasi-metric space of non-homogeneous type.
Highlights
Introduction and main resultsThe boundedness of fractional integral operators on the classical Morrey spaces was studied by Adams [ ], Chiarenza and Frasca et al [ ]
In [ ], by establishing a pointwise estimate of fractional integrals in terms of the Hardy-Littlewood maximal function, they showed the boundedness of fractional integral operators on the Morrey spaces
In, Sawano and Tanaka [ ] gave a natural definition of Morrey spaces for Radon measures which might be non-doubling but satisfied the growth condition, and they investigated the boundedness in these spaces of some classical operators in harmonic analysis
Summary
We consider the multilinear fractional integral operator, the multilinear Calderón-Zygmund operator and the multi-sublinear maximal operator. The multilinear fractional integral is defined by. Let T be a multilinear operator initially defined on the m-fold product of Schwartz spaces and taking values into the space of tempered distributions. Following [ ], we say that T is an m-linear Calderón-Zygmund operator if it extends to a bounded multilinear operator from Lp (X, μ) × Lp (X, μ) × · · · × Lpm (X, μ) to Lp(X, μ) for some ≤ p , . K, the so-called multilinear Calderón-Zygmund kernel, defined away from the diagonal x = y = · · · = ym in Xm+ , satisfying. ) is replaced by φi(u) ≤ C φi(v) for u ≥ v with the constant C > , the theorem is valid.
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