817 research outputs found
Hardy type inequality in variable Lebesgue spaces
We prove that in variable exponent spaces , where
satisfies the log-condition and is a bounded domain in
with the property that has
the cone property, the validity of the Hardy type inequality |
1/\delta(x)^\alpha \int_\Omega \phi(y) dy/|x-y|^{n-\alpha}|_{p(\cdot)} \leqq C
|\phi|_{p(\cdot)}, \quad 0<\al<\min(1,\frac{n}{p_+}), where
, is equivalent to a certain
property of the domain \Om expressed in terms of \al and \chi_\Om.Comment: 16 page
Orlicz-Hardy inequalities
We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus
extending results of Ancona, Lewis, and Wannebo
Orlicz-Hardy inequalities
We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus
extending results of Ancona, Lewis, and Wannebo
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