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SOME FRIEDRICHS TYPE INEQUALITIES IN THE FULL EUCLIDEAN SPACE

$icon-email$ JU. A. DUBINSKII

Abstract

In this paper we prove the inequality $\int_{R^{n}} μ_{R} (| x |) | u (x) |^{p} d x ⩽ M [\int_{R^{n}} | \nabla u (x) |^{p} ω (| x |) d x + {| \int_{| x | = R} u (x) d s |}^{p}],$ where $ω (| x |) > 0$ and $μ_{R} (| x |) > 0$ are the weight functions, $R > 0$ is an arbitrary number. In doing so, we first show some ”two-sides” Hardy type inequalities.

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SOME FRIEDRICHS TYPE INEQUALITIES IN THE FULL EUCLIDEAN SPACE

Abstract