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).
Original language | English |
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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