On L¹-Functions with a very Singular Behavior

2010/10/04 by Alexander A. Kovalevsky, Kovalevsky, Alexander A.
Mathematics · #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Mathematical Approximation and Integration #math.CA #msc:26B35 #msc:40A30 #msc:49J45

paper · pdf · doi:10.48550/arxiv.1010.0570

23 pages

arxiv created 2010/10/04 · arxiv updated 2010/10/05

Abstract

We give examples of L¹-functions that are essentially unbounded on every nonempty open subset of their domains of definition. We obtain such functions as limits of weighted sums of functions with the unboundedly increasing number of singular points lying at the nodes of standard compressible periodic grids in \Bbb Rⁿ. Moreover, we prove that the latter (basic) functions possess properties of uniform integral boundedness but do not have a pointwise majorant. Some applications of the main results are given.

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