3 citations · 10 across the 14 of their papers we have counts for
14 papers
Critical Caffarelli-Kohn-Nirenberg inequalities via nonlinear scaling argument
Megumi Sano, Yerkin Shaimerdenov, Hinako Sugimura
We show functional inequalities with logarithmic weights as a critical case of Caffarelli-Kohn-Nirenberg inequalities. Original CKN inequalities have polynomial weights and are sho…
A simple proof of attainability for the Sobolev inequality
Megumi Sano
We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.
Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
Masahiro Ikeda, Megumi Sano, Koichi Taniguchi
We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces $\dot{W}^{1,p}_{0, \te…
On eigenvalue problems involving the critical Hardy potential and Sobolev type inequalities with logarithmic weights in two dimensions
Megumi Sano, Futoshi Takahashi
We consider the two-dimensional eigenvalue problem for the Laplacian with the Neumann boundary condition involving the critical Hardy potential. We prove the existence of the secon…
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…
Critical Hardy inequality on the half-space via the harmonic transplantation
Megumi Sano, Futoshi Takahashi
We prove a critical Hardy inequality on the half-space by using the harmonic transplantation. Also we give an improvement of the subcritical Hardy inequality on the half-space, whi…
Improvements and generalizations of two Hardy type inequalities and their applications to the Rellich type inequalities
Megumi Sano
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy t…
Explicit optimal constants of two critical Rellich inequalities for radially symmetric functions
Megumi Sano
We consider two critical Rellich inequalities with singularities at both the origin and the boundary in the higher order critical radial Sobolev spaces , w…
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…
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.…
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…
Extremal functions of generalized critical Hardy inequalities
Megumi Sano
In this paper, we show the existence and non-existence of minimizers of the following minimization problems which include an open problem mentioned by Horiuchi and Kumlin in 2012:…
Finsler Hardy inequalities
A. Mercaldo, M. Sano, F. Takahashi
In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a poi…
Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation
Megumi Sano, Futoshi Takahashi
In this paper, we show a weighted Hardy inequality in a limiting case for functions in weighted Sobolev spaces with respect to an invariant measure. We also prove that the constant…