IJPAM: Volume 71, No. 3 (2011)

INTERPOLATION INEQUALITIES IN POWER TYPE
WEIGHTED LEBESGUE-SOBOLEV SPACES

B. Cekic$^1$, G. Alisoy$^2$, R.A. Mashiyev$^3$
$^{1,3}$Department of Mathematics
Dicle University
21280, Diyarbakir, TURKEY
$^2$Department of Mathematical Sciences
Inonu University
44280, Malatya, TURKEY


Abstract. In this paper we prove some interpolation inequalities between functions and their derivatives in the class of power type weighted Lebesgue-Sobolev spaces defined on bounded open subset $\Omega\subset R^{N}.$ As application of our results, we give a compact embedding theorem in power type weighted Sobolev space.

Received: March 30, 2011

AMS Subject Classification: 46E35, 46B70, 26D10

Key Words and Phrases: Lebesgue-Sobolev spaces, interpolation, power weight functions, compact embedding

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 3