- Hacettepe Journal of Mathematics and Statistics
- Vol: 46 Issue: 2
- A multiplier related to symmetric stable processes
A multiplier related to symmetric stable processes
Authors : Deniz Karli
Pages : 217-228
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Publication Date : 2017-04-01
Article Type : Research
Abstract :In two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a $d$- dimensional rotationally symmetric stable process. These results allow one to discuss some boundedness conditions with weaker hypotheses. In this paper, we study a multiplier theorem using these more general results. We consider a product process consisting of a $d$-dimensional symmetric stable process and a 1-dimensional Brownian motion, and use properties of jump processes to obtain bounds on jump terms and the $L^p(\mathbb{R}^d)$-norm of a new operator.Keywords : symmetric stable process, Fourier multiplier, harmonic extension, bounded operator