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A class of pairs of weights related to the boundedness of the Fractional Integral Operator between L p and Lipschitz spaces

Gladis Pradolini (2001)

Commentationes Mathematicae Universitatis Carolinae

In [P] we characterize the pairs of weights for which the fractional integral operator I γ of order γ from a weighted Lebesgue space into a suitable weighted B M O and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of I γ acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare...

A class of tridiagonal operators associated to some subshifts

Christian Hernández-Becerra, Benjamín A. Itzá-Ortiz (2016)

Open Mathematics

We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N....

A class of weighted convolution Fréchet algebras

Thomas Vils Pedersen (2010)

Banach Center Publications

For an increasing sequence (ωₙ) of algebra weights on ℝ⁺ we study various properties of the Fréchet algebra A(ω) = ⋂ ₙ L¹(ωₙ) obtained as the intersection of the weighted Banach algebras L¹(ωₙ). We show that every endomorphism of A(ω) is standard, if for all n ∈ ℕ there exists m ∈ ℕ such that ω m ( t ) / ω ₙ ( t ) → ∞ as t → ∞. Moreover, we characterise the continuous derivations on this algebra: Let M(ωₙ) be the corresponding weighted measure algebras and let B(ω) = ⋂ ₙM(ωₙ). If for all n ∈ ℕ there exists m ∈ ℕ such that...

A comprehensive proof of localization for continuous Anderson models with singular random potentials

François Germinet, Abel Klein (2013)

Journal of the European Mathematical Society

We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution),...

A counterexample in operator theory

Antonio Córdoba (1993)

Publicacions Matemàtiques

The purpose of this note is to give an explicit construction of a bounded operator T acting on the space L2[0,1] such that |Tf(x)| ≤ ∫01 |f(y)| dy for a.e. x ∈ [0.1], and, nevertheless, ||T||Sp = ∞ for every p < 2. Here || ||Sp denotes the norm associated to the Schatten-Von Neumann classes.

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