Search results for " 42B30"
showing 2 items of 2 documents
New Orlicz-Hardy Spaces Associated with Divergence Form Elliptic Operators
2009
Let $L$ be the divergence form elliptic operator with complex bounded measurable coefficients, $\omega$ the positive concave function on $(0,\infty)$ of strictly critical lower type $p_\oz\in (0, 1]$ and $\rho(t)={t^{-1}}/\omega^{-1}(t^{-1})$ for $t\in (0,\infty).$ In this paper, the authors study the Orlicz-Hardy space $H_{\omega,L}({\mathbb R}^n)$ and its dual space $\mathrm{BMO}_{\rho,L^\ast}({\mathbb R}^n)$, where $L^\ast$ denotes the adjoint operator of $L$ in $L^2({\mathbb R}^n)$. Several characterizations of $H_{\omega,L}({\mathbb R}^n)$, including the molecular characterization, the Lusin-area function characterization and the maximal function characterization, are established. The …
Pointwise characterizations of Hardy-Sobolev functions
2006
We establish simple pointwise characterizations of functions in the Hardy-Sobolev spaces within the range n/(n+1)<p <=1. In addition, classical Hardy inequalities are extended to the case p <= 1.