An atomic decomposition for the Bergman space of temperature functions on a cylinder

Marcos López-García

An atomic decomposition for the Bergman space of temperature functions on a cylinder

Marcos López-García

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

Abstract

For 1 ≤ p < ∞, we define the weighted Bergman space b _β^p(S_T) as consisting of the temperature functions on the cylinder S_T = S¹ × (0, T) that belong to L^p(Ω_T, t^βdxdt), where Ω_T = (0, 2) × (0, T). For α > β > -1 we construct a family of bounded projections P_α: L ¹(Ω_T, t^βdxdt) → b _β¹(S_T). We use this to get an atomic decomposition of the Bergman space b^p(S_T) = b ₀^p(S_T) for all p ≥ 1.

Original language	English
Pages (from-to)	101-119
Number of pages	19
Journal	Boletin de la Sociedad Matematica Mexicana
Volume	11
Issue number	1
State	Published - Apr 2005
Externally published	Yes

Keywords

Atomic decomposition
Bergman space

Cite this

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abstract = "For 1 ≤ p < ∞, we define the weighted Bergman space b βp(ST) as consisting of the temperature functions on the cylinder ST = S1 × (0, T) that belong to Lp(ΩT, tβdxdt), where ΩT = (0, 2) × (0, T). For α > β > -1 we construct a family of bounded projections Pα: L 1(ΩT, tβdxdt) → b β1(ST). We use this to get an atomic decomposition of the Bergman space bp(ST) = b 0p(ST) for all p ≥ 1.",

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N2 - For 1 ≤ p < ∞, we define the weighted Bergman space b βp(ST) as consisting of the temperature functions on the cylinder ST = S1 × (0, T) that belong to Lp(ΩT, tβdxdt), where ΩT = (0, 2) × (0, T). For α > β > -1 we construct a family of bounded projections Pα: L 1(ΩT, tβdxdt) → b β1(ST). We use this to get an atomic decomposition of the Bergman space bp(ST) = b 0p(ST) for all p ≥ 1.

AB - For 1 ≤ p < ∞, we define the weighted Bergman space b βp(ST) as consisting of the temperature functions on the cylinder ST = S1 × (0, T) that belong to Lp(ΩT, tβdxdt), where ΩT = (0, 2) × (0, T). For α > β > -1 we construct a family of bounded projections Pα: L 1(ΩT, tβdxdt) → b β1(ST). We use this to get an atomic decomposition of the Bergman space bp(ST) = b 0p(ST) for all p ≥ 1.

KW - Atomic decomposition

KW - Bergman space

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M3 - Artículo

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JO - Boletin de la Sociedad Matematica Mexicana

JF - Boletin de la Sociedad Matematica Mexicana

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An atomic decomposition for the Bergman space of temperature functions on a cylinder

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