On the behavior of integrable functions at infinity

2016/01/06 by Andrzej Komisarski, Komisarski, Andrzej
Mathematics · #26A42 #28A25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 26B15 #Secondary 40A05 #math.CA #msc:26A42 #msc:26B15 #msc:28A25 #msc:40A05

paper · pdf · doi:10.48550/arxiv.1601.01241

arxiv created 2016/01/06 · arxiv updated 2016/01/07

Abstract

We investigate the behavior of sequences (f(c_nx)) for Lebesgue integrable functions f:\mathbb R^d→\mathbb R. In particular, we give a~description of classes of multipliers (c_n) and (d_n) such that f(c_nx)→0 or ∑_n=1^∞|f(d_nx)|<∞ for λ almost every x∈\mathbb R^d.

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