Convolution in Weighted Lorentz Spaces of Type $\Gamma$

• Autores: Martin Krepela
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 119, Nº 1, 2016, págs. 113-132
• Idioma: inglés
• DOI: 10.7146/math.scand.a-24187
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• Resumen

  • We characterize boundedness of the convolution operator between weighted Lorentz spaces $\Gamma^p(v)$ and $\Gamma^q(w)$ for the range of parameters $p,q\in[1,\infty]$, or $p\in(0,1)$ and $q\in\{1,\infty\}$, or $p=\infty$ and $q\in(0,1)$. We provide Young-type convolution inequalities of the form \[ \|f\ast g\|_{\Gamma^q(w)} \le C \|f\|_{\Gamma^p(v)}\|g\|_Y, \quad f\in\Gamma^p(v), g\in Y, \] characterizing the optimal rearrangement-invariant space $Y$ for which the inequality is satisfied.