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An Extension of a Boundedness Result for Singular Integral Operators
Deniz Karli · 2015-01-21 · via math.PR updates on arXiv.org

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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