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Sobolev type inequalities for fractional maximal functions and Riesz potentials in Morrey spaces of variable exponent on half spaces

Yoshihiro Mizuta, Tetsu Shimomura (2023)

Czechoslovak Mathematical Journal

Our aim is to establish Sobolev type inequalities for fractional maximal functions M , ν f and Riesz potentials I , α f in weighted Morrey spaces of variable exponent on the half space . We also obtain Sobolev type inequalities for a C 1 function on . As an application, we obtain Sobolev type inequality for double phase functionals with variable exponents Φ ( x , t ) = t p ( x ) + ( b ( x ) t ) q ( x ) , where p ( · ) and q ( · ) satisfy log-Hölder conditions, p ( x ) < q ( x ) for x , and b ( · ) is nonnegative and Hölder continuous of order θ ( 0 , 1 ] .

Sobolev-Besov spaces of measurable functions

Hans Triebel (2010)

Studia Mathematica

The paper deals with spaces L p s ( ) of Sobolev type where s > 0, 0 < p ≤ ∞, and their relations to corresponding spaces B p , q s ( ) of Besov type where s > 0, 0 < p ≤ ∞, 0 < q ≤ ∞, in terms of embedding and real interpolation.

Sobolev-Kantorovich Inequalities

Michel Ledoux (2015)

Analysis and Geometry in Metric Spaces

In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means...

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