On the Rate of Almost Everywhere Convergence of Abel-Cartwright means on L p(R n)

Alexander M. Stokolos; Walter Trebels

doi:10.1007/BF03322062

On the Rate of Almost Everywhere Convergence of Abel-Cartwright means on L ^p(Rⁿ)

Alexander M. Stokolos
, Walter Trebels

Mathematical Sciences

Odessa National University
Technische Universität Darmstadt

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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,γf of the multidimensional Fourier integral. A typical result for these means is the following: Let γ>0 and fεBsp,p(Rn)where 0<s<γ,1<p<∞.&rthree;e Then, for almost all x ∈ R n, Wt,γf (x)−f(x)=ox,γ(ts), t→0+ &rthree;e.</div>

Original language	English
Pages (from-to)	373-380
Number of pages	8
Journal	Results in Mathematics
Volume	34
Issue number	3-4
DOIs	https://doi.org/10.1007/BF03322062
State	Published - Nov 1 1998

Scopus Subject Areas

Mathematics (miscellaneous)
Applied Mathematics

Keywords

Moduli of continuity of higher order
maximal functions
rate of almost everywhere convergence

Access to Document

10.1007/BF03322062License: Unspecified

Cite this

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title = "On the Rate of Almost Everywhere Convergence of Abel-Cartwright means on L p(R n)",

abstract = " The main purpose of this article is to establish results concerning the rate of almost everywhere convergence of the Abel-Cartwright means W t,\γf of the multidimensional Fourier integral. A typical result for these means is the following: Let \γ>0 and f\εBsp,p(Rn)where 0<s<\γ,1<p<\∞.\&rthree;e Then, for almost all x \∈ R n, Wt,\γf (x)\−f(x)=ox,\γ(ts), t\→0+ \&rthree;e.",

keywords = "Moduli of continuity of higher order, maximal functions, rate of almost everywhere convergence",

author = "Stokolos, \{Alexander M.\} and Walter Trebels",

note = "Publisher Copyright: {\textcopyright} 1998, Birkh/:auser Verlag, Basel.",

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T1 - On the Rate of Almost Everywhere Convergence of Abel-Cartwright means on L p(R n)

AU - Stokolos, Alexander M.

AU - Trebels, Walter

PY - 1998/11/1

Y1 - 1998/11/1

N2 - The main purpose of this article is to establish results concerning the rate of almost everywhere convergence of the Abel-Cartwright means W t,γf of the multidimensional Fourier integral. A typical result for these means is the following: Let γ>0 and fεBsp,p(Rn)where 0<s<γ,1<p<∞.&rthree;e Then, for almost all x ∈ R n, Wt,γf (x)−f(x)=ox,γ(ts), t→0+ &rthree;e.

AB - The main purpose of this article is to establish results concerning the rate of almost everywhere convergence of the Abel-Cartwright means W t,γf of the multidimensional Fourier integral. A typical result for these means is the following: Let γ>0 and fεBsp,p(Rn)where 0<s<γ,1<p<∞.&rthree;e Then, for almost all x ∈ R n, Wt,γf (x)−f(x)=ox,γ(ts), t→0+ &rthree;e.

KW - Moduli of continuity of higher order

KW - maximal functions

KW - rate of almost everywhere convergence

UR - https://www.scopus.com/pages/publications/0347166304

U2 - 10.1007/BF03322062

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M3 - Article

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JO - Results in Mathematics

JF - Results in Mathematics

IS - 3-4

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