The radial lemma of Strauss in the context of Morrey spaces

Sickel, Winfried; Yang, Dachun; Yuan, Wen

doi:10.5186/aasfm.2014.3918

Cited by 8 publications

(2 citation statements)

References 43 publications

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“…Later many authors studied subspaces consisted of radial elements in different function spaces cf. [6,22,23,24]. In particular asymptotic behaviour of entropy numbers of compact Sobolev embeddings of radial subspaces of Besov and Triebel-Lizorkin spaces were described by Th.…”

Section: Introductionmentioning

confidence: 99%

Some properties of block-radial functions and Schrödinger type operators with block-radial potentials

Dota

Skrzypczak

2019

Journal of Complexity

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Let R γ B s p,q (R d ) be a subspace of the Besov space B s p,q (R d ) that consists of block-radial functions. We prove that the asymptotic behaviour of the entropy numbers of compact embeddings id :depends on the number of blocks of the lowest dimension, the parameters p 1 and p 2 , but is independent of the smoothness parameters s 1 , s 2 . We apply the asymptotic behaviour to estimation of powers of a negative spectra of Schrödinger type operators with block-radial potentials. This part essentially relies on the Birman-Schwinger principle.

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Section: Introductionmentioning

confidence: 99%

Some properties of block-radial functions and Schrödinger type operators with block-radial potentials

Dota

Skrzypczak

2019

Journal of Complexity

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“…Then the Morrey-Sobolev embedding for radial functions (see e.g. [35,Proposition 1.1]) guarantees that the function , defined by (3.6), belongs to 1,∞ loc (R + ). Moreover, since…”

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confidence: 99%

A characterization of singular Schrödinger operators on the half-line

Scandone

Baglini²,

Simonov³

2020

Can. Math. Bull.

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We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of Schrödinger operators with potentials of very large (infinite) magnitude and very short (infinitesimal) range. As a consequence, we also derive a similar result for point interactions in the Euclidean space $\mathbb {R}^3$ , in the case of radial potentials. Moreover, we discuss explicitly our results in the case of potentials that are linear in a neighborhood of the origin.

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Strauss and Lions Type Theorems for the Fractional Sobolev Spaces with Variable Exponent and Applications to Nonlocal Kirchhoff–Choquard Problem

Bahrouni

Ounaies

2021

Mediterr. J. Math.

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The radial lemma of Strauss in the context of Morrey spaces

Cited by 8 publications

References 43 publications

Some properties of block-radial functions and Schrödinger type operators with block-radial potentials

Some properties of block-radial functions and Schrödinger type operators with block-radial potentials

A characterization of singular Schrödinger operators on the half-line

Strauss and Lions Type Theorems for the Fractional Sobolev Spaces with Variable Exponent and Applications to Nonlocal Kirchhoff–Choquard Problem

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