An extension of a boundedness result for singular integral operators

• Autorzy: Deniz Karlı
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60J45: Probabilistic potential theory
• 42A61: Probabilistic methods
• 60G46: Martingales and classical analysis

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 145
• Numer: 1
• Strony: 15-33

Daty

wydano

2016

Twórcy

autor

Deniz Karlı

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

Identyfikatory

DOI

10.4064/cm6722-1-2016