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math.FA2019★ 3 cited
Two limits on Hardy and Sobolev inequalities
Megumi Sano
It is known that classical Hardy and Sobolev inequalities hold when the exponent and the dimension satisfy . In this note, we consider two limits of Hardy a…
math.AP2019
Minimization problem associated with an improved Hardy-Sobolev type inequality
Megumi Sano
We consider the existence and the non-existence of a minimizer of the following minimization problems associated with an improved Hardy-Sobolev type inequality introduced by Ioku.…
math.AP2019
Remarks on a limiting case of Hardy type inequalities
Megumi Sano, Takuya Sobukawa
The classical Hardy inequality holds in Sobolev spaces when . In the limiting case where , it is known that by adding a logarithmic function to the Hard…