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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

40 Citations (Scopus)

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 ≤. © Copyright by Theta, 2008.

Original language	English
Pages (from-to)	309-332
Journal	Journal of Operator Theory
Volume	59
Issue number	2
Publication status	Published - 1 Jan 2008

Keywords

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

Cite this

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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.",

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year = "2008",

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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

Abstract

Keywords

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