On the Rate of Almost Everywhere Convergence of Abel-Cartwright Means of Lᵖ (ℝⁿ)

Alexander M. Stokolos, Walter Trebels

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Abstract

<div class="line" id="line-5"> The main purpose of this article is to establish results concerning the rate of almost everywhere convergence of the Abel-Cartwright means W t,&gamma;f of the multidimensional Fourier integral. A typical result for these means is the following: Let &gamma;&gt;0 and f&epsilon;Bsp,p(Rn)where 0&lt;s&lt;&gamma;,1&lt;p&lt;&infin;.&rthree;e Then, for almost all x &isin; R n, Wt,&gamma;f (x)&minus;f(x)=ox,&gamma;(ts), t&rarr;0+ &rthree;e.</div>
Original languageAmerican English
JournalResults in Mathematics
Volume34
DOIs
StatePublished - Nov 1998

Keywords

  • Convergence of Abel-Cartwright Means

DC Disciplines

  • Mathematics

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