Pointwise characterizations of Hardy-Sobolev functions

• Autores: Pekka Koskela , Eero Saksman
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 4, 2008, págs. 727-744
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n4.a11
• Texto completo no disponible (Saber más ...)
• Resumen

  • We establish pointwise characterizations of functions in the Hardy-Sobolev spaces $ H^{1,p}$ within the range $p\in (n/(n+1),1]$. In particular, a locally integrable function $u$ belongs to $ H^{1,p}(\real^n)$ if and only if $u\in L^p(\real^n)$ and it satisfies the Haj\l{}asz type condition $$ |u(x)-u(y)|\leq |x-y|(h(x)+h(y)),\quad x,y\in \real^n\setminus E, $$ where $E$ is a set of measure zero and $h\in L^p(\real^n)$. We also investigate Hardy-Sobolev spaces on subdomains and extend Hardy inequalities to the case $p\leq 1.$