Hilbert transform and singular integrals on the spaces of tempered ultradistributions

• Autorzy: Andrzej Kamiński , Dušanka Perišić , Stevan Pilipović
• Języki publikacji: EN

Abstrakty

EN

The Hilbert transform on the spaces $S'*(R^d)$ of tempered ultradistributions is defined, uniquely in the sense of hyperfunctions, as the composition of the classical Hilbert transform with the operators of multiplying and dividing a function by a certain elliptic ultrapolynomial. We show that the Hilbert transform of tempered ultradistributions defined in this way preserves important properties of the classical Hilbert transform. We also give definitions and prove properties of singular integral operators with odd and even kernels on the spaces $S'*(R^d)$, whose special cases are the Hilbert transform and Riesz operators.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 53
• Numer: 1
• Strony: 139-153

Daty

wydano

2000

Twórcy

autor

Andrzej Kamiński

• Institute of Mathematics, University of Rzeszów, Rejtana 16 C, 35-310 Rzeszów, Poland

autor

Dušanka Perišić

• Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Yugoslavia

autor

Stevan Pilipović

• Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Yugoslavia

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