An extension of a boundedness result for singular integral operators
Tom 145 / 2016
Colloquium Mathematicum 145 (2016), 15-33
MSC: Primary 60J45; Secondary 42A61, 60G46.
DOI: 10.4064/cm6722-1-2016
Opublikowany online: 30 March 2016
Streszczenie
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.
