Abstract
Recently, Abtahi, Nasr-Isfahani, and Rejali [1] have shown that if G is a locally compact but not compact topological group and p > 2, then there are two functions, f and g, such that the convolution \({f\star g}\) is equal to ∞ on some set of positive measure. In the paper we show the nonexistence of \({f\star g}\) on a set of positive measure for (f, g) from a complement of a σ-porous set.
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The work of the first author has been supported by the Polish Ministry of Science and Higher Education Grant No. N N201 414939.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Gła̧b, S., Strobin, F. Porosity and the L p-conjecture. Arch. Math. 95, 583–592 (2010). https://doi.org/10.1007/s00013-010-0189-y
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DOI: https://doi.org/10.1007/s00013-010-0189-y