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arXiv · 1501.05164

An Extension of a Boundedness Result for Singular Integral Operators

Deniz Karli
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Abstract

In this paper, we study some operators which are originated from classical Littlewood-Paley theory. We consider their modification with respect to our discontinuous setup, where the underlying process is the product of a one dimensional Brownian motion and a d-dimensional symmetric stable process. Two operators in focus are G-star and Area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on L^p. Moreover, we generalise a classical multiplier theorem by weakening its conditions on the tail of the kernel of singular integrals.

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Deniz Karli. 2016-01-16. An Extension of a Boundedness Result for Singular Integral Operators. https://doi.org/10.4064/cm6722-1-2016

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