2 citations · 3 across the 5 of their papers we have counts for
4 papers
On the compactness of the (non)radial Sobolev spaces
Shuji Machihara, Megumi Sano
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an…
Remarks on the Rellich inequality
Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade
We study the Rellich inequalities in the framework of equalities. We present equalities which imply the Rellich inequalities by dropping remainders. This provides a simple and dire…
Remarks on the Hardy type inequalities with remainder terms in the framework of equalities
Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade
We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultane…
Extremisers for the trace theorem on the sphere
Neal Bez, Shuji Machihara, Mitsuru Sugimoto
We find all extremisers for the trace theorem on the sphere. We also provide a sharp extension for functions belonging to certain Sobolev spaces with angular regularity.