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Nikolskii-type inequalities for trigonometric polynomials and entire functions of exponential type

Published online by Cambridge University Press:  09 April 2009

R. J. Nessel  and
G. Wilmes
R. J. Nessel
Affiliation:
Technical University of AachenAachen 51, Templergraben 55 Federal RepublicGermany
G. Wilmes
Affiliation:
Technical University of AachenAachen 51, Templergraben 55 Federal RepublicGermany
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Abstract

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Nikolskii-type inequalities, thus inequalities between different metrics of a function, are established for trigonometric polynomials and pth power integrable functions, 0<p<∞, of several variables having Fourier transform with compact support. It is shown that certain gaps in the spectra of the functions involved may be taken into account. As an immediate consequence it follows that the general results cover the classical inequalities which are concerned with functions of rectangular type. But at the same time one may give applications to functions of type K where K is a symmetric body in Euclidean n–space.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 7 - 18
Copyright
Copyright © Australian Mathematical Society 1978

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