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An extension of a boundedness result for singular integral operators

Volume 145 / 2016

Deniz Karlı Colloquium Mathematicum 145 (2016), 15-33 MSC: Primary 60J45; Secondary 42A61, 60G46. DOI: 10.4064/cm6722-1-2016 Published online: 30 March 2016


We study some operators originating 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 the $G^{*}$ and area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on $L^p$. Moreover, we generalize a classical multiplier theorem by weakening its conditions on the tail of the kernel of singular integrals.


  • Deniz KarlıDepartment of Mathematics
    Işık University
    AMF233, 34980 Şile, Istanbul, Turkey

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