Displaying similar documents to “Hardy-Sobolev Inequalities for Hessian Integrals”

A new characterization of the Sobolev space

Piotr Hajłasz (2003)

Studia Mathematica

Similarity:

The purpose of this paper is to provide a new characterization of the Sobolev space W 1 , 1 ( ) . We also show a new proof of the characterization of the Sobolev space W 1 , p ( ) , 1 ≤ p < ∞, in terms of Poincaré inequalities.

Sharp L p -weighted Sobolev inequalities

Carlos Pérez (1995)

Annales de l'institut Fourier

Similarity:

We prove sharp weighted inequalities of the form R n | f ( x ) | p v ( x ) d x C R n | q ( D ) ( f ) ( x ) | p N ( v ) ( x ) d x where q ( D ) is a differential operator and N is a combination of maximal type operator related to q ( D ) and to p .

On a variant of the Hardy inequality between weighted Orlicz spaces

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2009)

Studia Mathematica

Similarity:

Let M be an N-function satisfying the Δ₂-condition, and let ω, φ be two other functions, with ω ≥ 0. We study Hardy-type inequalities M ( ω ( x ) | u ( x ) | ) e x p ( - φ ( x ) ) d x C M ( | u ' ( x ) | ) e x p ( - φ ( x ) ) d x , where u belongs to some set of locally absolutely continuous functions containing C ( ) . We give sufficient conditions on the triple (ω,φ,M) for such inequalities to be valid for all u from a given set . The set may be smaller than the set of Hardy transforms. Bounds for constants are also given, yielding classical Hardy inequalities with best constants. ...

Moser-Trudinger and logarithmic HLS inequalities for systems

Itai Shafrir, Gershon Wolansky (2005)

Journal of the European Mathematical Society

Similarity:

We prove several optimal Moser–Trudinger and logarithmic Hardy–Littlewood–Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere S 2 , on a bounded domain Ω 2 and on all of 2 . In some cases we also address the question of existence of minimizers.

Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces

Robert Černý (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let n 2 and Ω n be a bounded set. We give a Moser-type inequality for an embedding of the Orlicz-Sobolev space W 0 L Φ ( Ω ) , where the Young function Φ behaves like t n log α ( t ) , α < n - 1 , for t large, into the Zygmund space Z 0 n - 1 - α n ( Ω ) . We also study the same problem for the embedding of the generalized Lorentz-Sobolev space W 0 m L n m , q log α L ( Ω ) , m < n , q ( 1 , ] , α < 1 q ' , embedded into the Zygmund space Z 0 1 q ' - α ( Ω ) .

Two-weighted criteria for integral transforms with multiple kernels

Vakhtang Kokilashvili, Alexander Meskhi (2006)

Banach Center Publications

Similarity:

Necessary and sufficient conditions governing two-weight L p norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.

Note on special arithmetic and geometric means

Horst Alzer (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove: If A ( n ) and G ( n ) denote the arithmetic and geometric means of the first n positive integers, then the sequence n n A ( n ) / G ( n ) - ( n - 1 ) A ( n - 1 ) / G ( n - 1 ) ( n 2 ) is strictly increasing and converges to e / 2 , as n tends to .

Sharp embedding results for spaces of smooth functions with power weights

Martin Meyries, Mark Veraar (2012)

Studia Mathematica

Similarity:

We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on d , equipped with power weights w ( x ) = | x | γ , γ > -d. We prove two-weight Sobolev embeddings for these spaces. Moreover, we precisely characterize for which parameters the embeddings hold. The proofs are presented in such a way that they also hold for vector-valued functions.

Sharp Logarithmic Inequalities for Two Hardy-type Operators

Adam Osękowski (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

For any locally integrable f on ℝⁿ, we consider the operators S and T which average f over balls of radius |x| and center 0 and x, respectively: S f ( x ) = 1 / | B ( 0 , | x | ) | B ( 0 , | x | ) f ( t ) d t , T f ( x ) = 1 / | B ( x , | x | ) | B ( x , | x | ) f ( t ) d t for x ∈ ℝⁿ. The purpose of the paper is to establish sharp localized LlogL estimates for S and T. The proof rests on a corresponding one-weight estimate for a martingale maximal function, a result which is of independent interest.

Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces

Dorothee D. Haroske (2011)

Banach Center Publications

Similarity:

We study continuity envelopes of function spaces B p , q s ( , w ) and F p , q s ( , w ) where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.

Variable exponent trace spaces

Lars Diening, Peter Hästö (2007)

Studia Mathematica

Similarity:

The trace space of W 1 , p ( · ) ( × [ 0 , ) ) consists of those functions on ℝⁿ that can be extended to functions of W 1 , p ( · ) ( × [ 0 , ) ) (as in the fixed-exponent case). Under the assumption that p is globally log-Hölder continuous, we show that the trace space depends only on the values of p on the boundary. In our main result we show how to define an intrinsic norm for the trace space in terms of a sharp-type operator.

The minimal operator and the geometric maximal operator in ℝⁿ

David Cruz-Uribe, SFO (2001)

Studia Mathematica

Similarity:

We prove two-weight norm inequalities in ℝⁿ for the minimal operator f ( x ) = i n f Q x 1 / | Q | Q | f | d y , extending to higher dimensions results obtained by Cruz-Uribe, Neugebauer and Olesen [8] on the real line. As an application we extend to ℝⁿ weighted norm inequalities for the geometric maximal operator M f ( x ) = s u p Q x e x p ( 1 / | Q | Q l o g | f | d x ) , proved by Yin and Muckenhoupt [27]. We also give norm inequalities for the centered minimal operator, study powers of doubling weights and give sufficient conditions for the geometric maximal operator to be equal...