Displaying similar documents to “Fractional Hardy-Sobolev-Maz'ya inequality for domains”

Fractional Hardy inequalities and visibility of the boundary

Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas (2014)

Studia Mathematica

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We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection with the boundedness of extension operators for fractional Sobolev spaces.

Fractional Hardy inequality with a remainder term

Bartłomiej Dyda (2011)

Colloquium Mathematicae

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We prove a Hardy inequality for the fractional Laplacian on the interval with the optimal constant and additional lower order term. As a consequence, we also obtain a fractional Hardy inequality with the best constant and an extra lower order term for general domains, following the method of M. Loss and C. Sloane [J. Funct. Anal. 259 (2010)].

Trace inequalities for fractional integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi (2012)

Studia Mathematica

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rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from L p ) , θ ( X , μ ) to L q ) , q θ / p ( X , ν ) (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace...

Essential normality for certain finite linear combinations of linear-fractional composition operators on the Hardy space H 2

Mahsa Fatehi, Bahram Khani Robati (2012)

Czechoslovak Mathematical Journal

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In 1999 Nina Zorboska and in 2003 P. S. Bourdon, D. Levi, S. K. Narayan and J. H. Shapiro investigated the essentially normal composition operator C ϕ , when ϕ is a linear-fractional self-map of 𝔻 . In this paper first, we investigate the essential normality problem for the operator T w C ϕ on the Hardy space H 2 , where w is a bounded measurable function on ∂ 𝔻 which is continuous at each point of F ( ϕ ) , ϕ ∈ 𝒮 ( 2 ) , and T w is the Toeplitz operator with symbol w . Then we use these results and characterize the essentially...

Suitable domains to define fractional integrals of Weyl via fractional powers of operators

Celso Martínez, Antonia Redondo, Miguel Sanz (2011)

Studia Mathematica

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We present a new method to study the classical fractional integrals of Weyl. This new approach basically consists in considering these operators in the largest space where they make sense. In particular, we construct a theory of fractional integrals of Weyl by studying these operators in an appropriate Fréchet space. This is a function space which contains the L p ( ℝ ) -spaces, and it appears in a natural way if we wish to identify these fractional operators with fractional powers of a suitable...

Boundedness of one-sided fractional integrals in the one-sided Calderón-Hardy spaces

Alejandra Perini (2011)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we study the mapping properties of the one-sided fractional integrals in the Calderón-Hardy spaces ℋ q , α p , + ( ω ) for 0 < p ≤ 1 , 0 < α < ∞ and 1 < q < ∞ . Specifically, we show that, for suitable values of p , q , γ , α and s , if ω ∈ A s + (Sawyer’s classes of weights) then the one-sided fractional integral I γ + can be extended to a bounded operator from ℋ q , α p , + ( ω ) to ℋ q , α + γ p , + ( ω ) . The result is a consequence of the pointwise inequality N q , α + γ + I γ + F ; x ≤ C α , γ N q , α + F ; x , where N q , α + ( F ; x ) denotes the Calderón maximal function.

Left general fractional monotone approximation theory

George A. Anastassiou (2016)

Applicationes Mathematicae

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We introduce left general fractional Caputo style derivatives with respect to an absolutely continuous strictly increasing function g. We give various examples of such fractional derivatives for different g. Let f be a p-times continuously differentiable function on [a,b], and let L be a linear left general fractional differential operator such that L(f) is non-negative over a closed subinterval I of [a,b]. We find a sequence of polynomials Qₙ of degree ≤n such that L(Qₙ) is non-negative...

Functions of finite fractional variation and their applications to fractional impulsive equations

Dariusz Idczak (2017)

Czechoslovak Mathematical Journal

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We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak σ -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a σ -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.