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Hilbert transform and singular integrals on the spaces of tempered ultradistributions

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Kamiński A., Perišić D., Pilipović S.

Banach Center Publications

2000

tom 53

nr 1

139-153

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.

Ograniczanie wyników

1 Banach Center Publications

1 Kamiński A.

1 Perišić D.

1 Pilipović S.

1 2000

Wyniki wyszukiwania

Hilbert transform and singular integrals on the spaces of tempered ultradistributions