We consider a product process consisting of a $d$-dimensionalsymmetric stable process and a 1-dimensional Brownian motion, and use properties of jump processes to obtain bounds on jump terms andthe $L^p(\mathbb{R}^d)$-norm of a new operator.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:We consider a product process consisting of a $d$-dimensionalsymmetric stable process and a 1-dimensional Brownian motion, and use properties of jump processes to obtain bounds on jump terms andthe $L^p(\mathbb{R}^d)$-norm of a new operator.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:symmetric stable process · Fourier multiplier · harmonic extension
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 $d$-dimensionalsymmetric stable process and a 1-dimensional Brownian motion, and use properties of jump processes to obtain bounds on jump terms andthe $L^p(\mathbb{R}^d)$-norm of a new operator.
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