Distorted Hankel integral operators

2002/12/20 by A. B. Aleksandrov, V. V. Peller, Aleksandrov, A. B. +1
Mathematics · #46E #46F #47B35 #47G10 #Category Theory (math.CT) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.CO #math.CT #math.CV #math.FA #msc:46E #msc:46F #msc:47B35 #msc:47G10

paper · pdf · doi:10.48550/arxiv.math/0212293

arxiv created 2002/12/20 · arxiv updated 2009/11/30

Abstract

For \a,\b>0 and for a locally integrable function (or, more generally, a distribution) \f on (0,\be), we study integral ooperators \frak G^\a,\b_\f on L²(\R₊) defined by (\frak G^\a,\b_\f f)(x)=∫_\R+\f(x^\a+y^\b)f(y)dy. We describe the bounded and compact operators \frak G^\a,\b_\f and operators \frak G^\a,\b_\f of Schatten--von Neumann class \bS_p. We also study continuity properties of the averaging projection \Q_\a,\b onto the operators of the form \frak G^\a,\b_\f. In particular, we show that if \a≤\b and \b>1, then \frak G^\a,\b_\f is bounded on \bS_p if and only if 2\b(\b+1)^-1<p<2\b(\b-1)^-1.

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