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2003•Hokkaido Mathematical JournalOpen access

Lp(Rn) boundedness for a class of g-functions and applications

Guoen Hu

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Abstract

A class of g-functions related to the commutators of convolution opera- tors are considered, a sufficient condition implying the L^{p}(\mathbb{R}^{n}) boundedness for these g-functions is obtained.As applications, some new results about the L^{p}(\mathbb{R}^{n}) bound- edness for the commutators of the Marcinkiewicz integrals and the maximal operators corresponding to the commutators of homogeneous singular integral operators are estab- lished.

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What this paper is about

A class of g-functions related to the commutators of convolution opera- tors are considered, a sufficient condition implying the L^{p}(\mathbb{R}^{n}) boundedness for these g-functions is obtained.As applications, some new results about the L^{p}(\mathbb{R}^{n}) bound- edness for the commutators of the Marcinkiewicz integrals and the maximal operators corresponding to the commutators of homogeneous singular integral operators are estab- lished.

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Available abstract

A class of g-functions related to the commutators of convolution opera- tors are considered, a sufficient condition implying the L^{p}(\mathbb{R}^{n}) boundedness for these g-functions is obtained.As applications, some new results about the L^{p}(\mathbb{R}^{n}) bound- edness for the commutators of the Marcinkiewicz integrals and the maximal operators corresponding to the commutators of homogeneous singular integral operators are estab- lished.

Key concepts: Mathematics, Singular integral operators, Homogeneous, Class (philosophy), Convolution (computer science), Pure mathematics, Singular integral, Pseudodifferential operators

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