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Search: MSC category 46E35 ( Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems )

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1. CMB 2008 (vol 51 pp. 236)

2. CMB 2004 (vol 47 pp. 540)

Jain, Pankaj; Jain, Pawan K.; Gupta, Babita
 Compactness of Hardy-Type Operators over Star-Shaped Regions in $\mathbb{R}^N$ We study a compactness property of the operators between weighted Lebesgue spaces that average a function over certain domains involving a star-shaped region. The cases covered are (i) when the average is taken over a difference of two dilations of a star-shaped region in $\RR^N$, and (ii) when the average is taken over all dilations of star-shaped regions in $\RR^N$. These cases include, respectively, the average over annuli and the average over balls centered at origin. Keywords:Hardy operator, Hardy-Steklov operator, compactness, boundedness, star-shaped regionsCategories:46E35, 26D10

3. CMB 2004 (vol 47 pp. 206)

Hurri-Syrjänen, Ritva
 The PoincarÃ© Inequality and Reverse Doubling Weights We show that Poincar\'e inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains. Keywords:reverse doubling weights, PoincarÃ© inequality, John domainsCategory:46E35

4. CMB 1998 (vol 41 pp. 257)

Bagby, Thomas; Gauthier, P. M.
 Note on the support of Sobolev functions We prove a topological restriction on the support of Sobolev functions. Categories:46E35, 31B05