Lattice-embedding scales ofL p spaces into orlicz spaces

Hernández, Francisco L.; Rodrı́guez-Salinas, Baltasar

doi:10.1007/bf02897064

Cited by 10 publications

(7 citation statements)

References 21 publications

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“…Another example of an Orlicz space with the properties (i), (ii) can be found in [29] although the constructions there were done for different purposes.…”

Section: 4mentioning

confidence: 98%

Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators

Djakov

Mityagin

2012

Journal of Functional Analysis

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We study the system of root functions (SRF) of Hill operator Ly = −y + vy with a singular (complexvalued) potential v ∈ H −1 per and the SRF of 1D Dirac operator Ly = i 1 0Q 0 , subject to periodic or anti-periodic boundary conditions. Series of necessary and sufficient conditions (in terms of Fourier coefficients of the potentials and related spectral gaps and deviations) for SRF to contain a Riesz basis are proven. Equiconvergence theorems are used to explain basis property of SRF in L p -spaces and other rearrangement invariant function spaces.

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“…Another example of an Orlicz space with the properties (i), (ii) can be found in [29] although the constructions there were done for different purposes.…”

Section: 4mentioning

confidence: 98%

Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators

Djakov

Mityagin

2012

Journal of Functional Analysis

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“…This follows directly from above and [15, Proposition 2.b.3]. These inequalities can be strict (see [11] for Orlicz sequence space examples). Next result follows easily by p -factorization: Proposition 5.1.…”

Section: Indices and Criteriamentioning

confidence: 53%

Strictly singular and strictly co-singular inclusions between symmetric sequence spaces

Hernández

Sánchez

Семенов

2004

Journal of Mathematical Analysis and Applications

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Strict singularity and strict co-singularity of inclusions between symmetric sequence spaces are studied. Suitable conditions are provided involving the associated fundamental functions. The special case of Lorentz and Marcinkiewicz spaces is characterized. It is also proved that if E → F are symmetric sequence spaces with E = 1 and F = c 0 and ∞ then there exist a intermediate symmetric sequence space G such that E → G → F and both inclusions are not strictly singular. As a consequence new characterizations of the spaces c 0 and 1 inside the class of all symmetric sequence spaces are given.

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“…There exist Orlicz function spaces L Φ (μ) containing latices-isomorphic copies of L p for a fixed 0 < p ≤ 1 (see Theorems A and A in [16]).…”

Section: Remarkmentioning

confidence: 99%

Problems of existence of order copies of $$\ell ^\infty $$ ℓ ∞ and $$L_p(\nu )$$ L p ( ν ) in some non-Banach Köthe spaces

et al. 2019

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For a monotone Orlicz function Φ taking only values 0 and ∞, it is showed that in both cases, the s-homogeneous norm • Φ,s , if Φ is s-convex (0 < s ≤ 1) and the Mazur-Orlicz F-norm • Φ , if Φ is non-decreasing on R + , we have that L Φ (μ) = L ∞ (μ) and both these norms are proportional to • ∞. The problems of existence of order linearly isometric copy of ∞ \B ∞ (0, ε) for any ε > 0 as well as an order linearly isometric copy of the whole ∞ in Orlicz F-normed function and sequence spaces are considered. In the last section the problem of the existence of order linearly isometric copies of L p (ν) with 0 < p ≤ 1 in F-normed Orlicz spaces are considered.

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Lattice-embedding scales ofL p spaces into orlicz spaces

Cited by 10 publications

References 21 publications

Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators

Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators

Strictly singular and strictly co-singular inclusions between symmetric sequence spaces

Problems of existence of order copies of $$\ell ^\infty $$ ℓ ∞ and $$L_p(\nu )$$ L p ( ν ) in some non-Banach Köthe spaces

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