Compactness of families of convolution operators with respect to convergence almost everywhere

Sergey Kostyukovsky; Alexander Olevskii

Compactness of families of convolution operators with respect to convergence almost everywhere

School of Mathematical Sciences

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

Abstract

For a given sequence of measures μ_n on the circle T weakly convergent to the Dirac measure, we ask, is it possible to extract a subsequence n(j) such that for any f in the space L¹(L²,L^∞) the convolutions f * μn(j) converge to f almost everywhere. We show that it is crucial whether the measures are absolutely continuous, discrete or singular (non-atomic).

Original language	English
Pages (from-to)	755-766
Number of pages	12
Journal	Real Analysis Exchange
Volume	30
Issue number	2
State	Published - 2004

Keywords

Almost everywhere convergence
Convolutions

Cite this

@article{68d30ddb467542b5a91845350324eb3d,

title = "Compactness of families of convolution operators with respect to convergence almost everywhere",

abstract = "For a given sequence of measures μn on the circle T weakly convergent to the Dirac measure, we ask, is it possible to extract a subsequence n(j) such that for any f in the space L1(L2,L∞) the convolutions f * μn(j) converge to f almost everywhere. We show that it is crucial whether the measures are absolutely continuous, discrete or singular (non-atomic).",

keywords = "Almost everywhere convergence, Convolutions",

author = "Sergey Kostyukovsky and Alexander Olevskii",

year = "2004",

language = "אנגלית",

volume = "30",

pages = "755--766",

journal = "Real Analysis Exchange",

issn = "0147-1937",

publisher = "Michigan State University Press",

number = "2",

}

TY - JOUR

T1 - Compactness of families of convolution operators with respect to convergence almost everywhere

AU - Kostyukovsky, Sergey

AU - Olevskii, Alexander

PY - 2004

Y1 - 2004

N2 - For a given sequence of measures μn on the circle T weakly convergent to the Dirac measure, we ask, is it possible to extract a subsequence n(j) such that for any f in the space L1(L2,L∞) the convolutions f * μn(j) converge to f almost everywhere. We show that it is crucial whether the measures are absolutely continuous, discrete or singular (non-atomic).

AB - For a given sequence of measures μn on the circle T weakly convergent to the Dirac measure, we ask, is it possible to extract a subsequence n(j) such that for any f in the space L1(L2,L∞) the convolutions f * μn(j) converge to f almost everywhere. We show that it is crucial whether the measures are absolutely continuous, discrete or singular (non-atomic).

KW - Almost everywhere convergence

KW - Convolutions

UR - http://www.scopus.com/inward/record.url?scp=79952907802&partnerID=8YFLogxK

M3 - מאמר

AN - SCOPUS:79952907802

VL - 30

SP - 755

EP - 766

JO - Real Analysis Exchange

JF - Real Analysis Exchange

SN - 0147-1937

IS - 2

ER -

Compactness of families of convolution operators with respect to convergence almost everywhere

Abstract

Keywords

Other files and links

Fingerprint

Cite this