An extension of a boundedness result for singular integral operators

Deniz Karlı¹

¹Department of Mathematics Işık University AMF233, 34980 Şile, Istanbul, Turkey

Colloquium Mathematicum, Tome 145 (2016) no. 1, pp. 15-33

Résumé

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.

Détail

DOI : 10.4064/cm6722-1-2016

Keywords: study operators originating classical littlewood paley theory consider their modification respect discontinuous setup where underlying process product one dimensional brownian motion d dimensional symmetric stable process operators focus * area functionals using results obtained previous paper these operators bounded nbsp moreover generalize classical multiplier theorem weakening its conditions tail kernel singular integrals