An extension of a boundedness result for singular integral operators

Deniz Karlı. "An extension of a boundedness result for singular integral operators." Colloquium Mathematicae 145.1 (2016): 15-33. <http://eudml.org/doc/286361>.

@article{DenizKarlı2016,
abstract = {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.},
author = {Deniz Karlı},
journal = {Colloquium Mathematicae},
keywords = {multiplier; symmetric stable process; singular integrals; probabilistic Littlewood-Paley functions; area functional; Gunctional},
language = {eng},
number = {1},
pages = {15-33},
title = {An extension of a boundedness result for singular integral operators},
url = {http://eudml.org/doc/286361},
volume = {145},
year = {2016},
}

TY - JOUR
AU - Deniz Karlı
TI - An extension of a boundedness result for singular integral operators
JO - Colloquium Mathematicae
PY - 2016
VL - 145
IS - 1
SP - 15
EP - 33
AB - 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.
LA - eng
KW - multiplier; symmetric stable process; singular integrals; probabilistic Littlewood-Paley functions; area functional; Gunctional
UR - http://eudml.org/doc/286361
ER -