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math.AP2024
Sobolev interpolation inequalities with optimal Hardy-Rellich inequalities and critical exponents
Nguyen Anh Dao, Anh Xuan Do, Nguyen Lam +1
We establish a new family of the critical higher order Sobolev interpolation inequalities for radial functions as well as for non-radial functions. These Sobolev interpolation ineq…
math.AP2024
Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space
Anh Xuan Do, Debdip Ganguly, Nguyen Lam +1
We establish a general scale-dependent Poincaré-Hardy type identity involving a vector field on the hyperbolic space. By choosing suitable parameter, potential and vector field in…