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
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AN - SCOPUS:79952907802
VL - 30
SP - 755
EP - 766
JO - Real Analysis Exchange
JF - Real Analysis Exchange
SN - 0147-1937
IS - 2
ER -