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 . Moreover, we generalize a classical multiplier theorem by weakening its conditions on the tail of the kernel of singular integrals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6722-1-2016,
author = {Deniz Karl\i },
title = {An extension of a boundedness result for singular integral operators},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {15-33},
zbl = {06602768},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6722-1-2016}
}
Deniz Karlı. An extension of a boundedness result for singular integral operators. Colloquium Mathematicae, Tome 144 (2016) pp. 15-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6722-1-2016/