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 Maddede Bu Makale
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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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