Weighted inequalities involving two hardy operators with applications to embeddings of function spaces

María Carro; Amiran Gogatishvili; Joaquim Martín; Luboš Pick

Weighted inequalities involving two hardy operators with applications to embeddings of function spaces

María Carro, Amiran Gogatishvili, Joaquim Martín, Luboš Pick

Departament de Matemàtiques

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Resum

We find necessary and sufficient conditions for the two-operator weighted inequality (Equation Presented). We use this inequality to study embedding properties between the function spaces Sp(u) equipped with the norm (Equation Presented) and the classical Lorentz spaces Λp(v) and Γq(w). Moreover, we solve the only missing open case of the embedding Λp (v) → Γq(W) where 0 ≪ q ≪ p ≤. © Copyright by Theta, 2008.

Idioma original	Anglès
Pàgines (de-a)	309-332
Revista	Journal of Operator Theory
Volum	59
Número	2
Estat de la publicació	Publicada - 1 de gen. 2008

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title = "Weighted inequalities involving two hardy operators with applications to embeddings of function spaces",

abstract = "We find necessary and sufficient conditions for the two-operator weighted inequality (Equation Presented). We use this inequality to study embedding properties between the function spaces Sp(u) equipped with the norm (Equation Presented) and the classical Lorentz spaces Λp(v) and Γq(w). Moreover, we solve the only missing open case of the embedding Λp (v) → Γq(W) where 0 ≪ q ≪ p ≤. {\textcopyright} Copyright by Theta, 2008.",

keywords = "Average operator, Classical lorentz spaces, Dual average operator, Embeddings, Spaces S (w) p, Two-operator weighted inequality, Weighted inequalities",

author = "Mar{\'i}a Carro and Amiran Gogatishvili and Joaquim Mart{\'i}n and Lubo{\v s} Pick",

year = "2008",

month = jan,

day = "1",

language = "English",

volume = "59",

pages = "309--332",

journal = "Journal of Operator Theory",

issn = "0379-4024",

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TY - JOUR

T1 - Weighted inequalities involving two hardy operators with applications to embeddings of function spaces

AU - Carro, María

AU - Gogatishvili, Amiran

AU - Martín, Joaquim

AU - Pick, Luboš

PY - 2008/1/1

Y1 - 2008/1/1

N2 - We find necessary and sufficient conditions for the two-operator weighted inequality (Equation Presented). We use this inequality to study embedding properties between the function spaces Sp(u) equipped with the norm (Equation Presented) and the classical Lorentz spaces Λp(v) and Γq(w). Moreover, we solve the only missing open case of the embedding Λp (v) → Γq(W) where 0 ≪ q ≪ p ≤. © Copyright by Theta, 2008.

AB - We find necessary and sufficient conditions for the two-operator weighted inequality (Equation Presented). We use this inequality to study embedding properties between the function spaces Sp(u) equipped with the norm (Equation Presented) and the classical Lorentz spaces Λp(v) and Γq(w). Moreover, we solve the only missing open case of the embedding Λp (v) → Γq(W) where 0 ≪ q ≪ p ≤. © Copyright by Theta, 2008.

KW - Average operator

KW - Classical lorentz spaces

KW - Dual average operator

KW - Embeddings

KW - Spaces S (w) p

KW - Two-operator weighted inequality

KW - Weighted inequalities

M3 - Article

SN - 0379-4024

VL - 59

SP - 309

EP - 332

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -

Weighted inequalities involving two hardy operators with applications to embeddings of function spaces

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