Quantitative functional calculus in Sobolev spaces

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dc.creatorMorosi, Carlo
dc.creatorPizzocchero, Livio
dc.date2003-05-23
dc.date2004-10-25
dc.date.accessioned2026-07-07T04:58:13Z
dc.date.available2026-07-07T04:58:13Z
dc.descriptionIn the framework of Sobolev (Bessel potential) spaces $H^n(\reali^d, \reali {or} \complessi)$, we consider the nonlinear Nemytskij operator sending a function $x \in \reali^d \mapsto f(x)$ into a composite function $x \in \reali^d \mapsto G(f(x), x)$. Assuming sufficient smoothness for $G$, we give a "tame" bound on the $H^n$ norm of this composite function in terms of a linear function of the $H^n$ norm of $f$, with a coefficient depending on $G$ and on the $H^a$ norm of $f$, for all integers $n, a, d$ with $a > d/2$. In comparison with previous results on this subject, our bound is fully explicit, allowing to estimate quantitatively the $H^n$ norm of the function $x \mapsto G(f(x),x)$. When applied to the case $G(f(x), x) = f^2(x)$, this bound agrees with a previous result of ours on the pointwise product of functions in Sobolev spaces.
dc.descriptionLaTex, 37 pages. Final version, differing only by minor typographical changes from the versions of May 23, 2003 and March 8, 2004
dc.identifierhttps://arxiv.org/abs/math/0305331
dc.identifierhttp://arxiv.org/abs/math/0305331
dc.identifierJournal of Function Spaces and Applications (JFSA) 2 (2004), 279-321
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67546
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.subject46E35, 26D10, 47A60
dc.titleQuantitative functional calculus in Sobolev spaces
dc.typetext

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