scholarly journals ON LITTLEWOOD-PALEY FUNCTIONS ASSOCIATED WITH BESSEL OPERATORS

2009 ◽  
Vol 51 (1) ◽  
pp. 55-70 ◽  
Author(s):  
J. J. BETANCOR ◽  
J. C. FARIÑA ◽  
A. SANABRIA
Keyword(s):  
Higher Order ◽  
Doubling Measure ◽  
Homogeneous Type ◽  
Type Space ◽  
Bessel Operators ◽  
Homogeneous Type Space

AbstractIn this paper, we study Lp-boundedness properties for higher order Littlewood-Paley g-functions in the Bessel setting. We use the Calderón-Zygmund theory in a homogeneous-type space (in the sense of Coifman and Weiss) ((0, ∞), d, γα), where d represents the usual metric on (0, ∞) and γα denotes the doubling measure on (0, ∞) with respect to d defined by dγα(x) = x2α+1dx, with α > −1/2.

scholarly journals Calderón–Zygmund Operators Associated to Ultraspherical Expansions

2007 ◽  
Vol 59 (6) ◽  
pp. 1223-1244 ◽  
Author(s):  
Dariusz Buraczewski ◽  
Teresa Martinez ◽  
José L. Torrea
Keyword(s):  
Differential Operator ◽  
Higher Order ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Type Space ◽  
Ultraspherical Expansions ◽  
Homogeneous Type Space

AbstractWe define the higher order Riesz transforms and the Littlewood–Paley g-function associated to the differential operator Lλf(θ) = –f′′(θ)–2λ cot θ f′(θ) + λ2f(θ). We prove that these operators are Calderón–Zygmund operators in the homogeneous type space ((0, π), (sin t)2λdt). Consequently, Lp weighted, H1 – L1 and L∞ – BMO inequalities are obtained.

scholarly journals Higher order Riesz transforms associated with Bessel operators

2008 ◽  
Vol 46 (2) ◽  
pp. 219-250 ◽  
Author(s):  
Jorge J. Betancor ◽  
Juan C. Fariña ◽  
Teresa Martinez ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Higher Order ◽  
Riesz Transforms ◽  
Bessel Operators

scholarly journals Pointwise Multipliers on Spaces of Homogeneous Type in the Sense of Coifman and Weiss

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanchang Han ◽  
Fanghui Liao ◽  
Zongguang Liu
Keyword(s):  
Orthonormal Basis ◽  
General Setting ◽  
Doubling Measure ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Pointwise Multipliers ◽  
Additional Assumptions

By applying the remarkable orthonormal basis constructed recently by Ausher and Hytönen on spaces of homogeneous type in the sense of Coifman and Weiss, pointwise multipliers of inhomogeneous Besov and Triebel-Lizorkin spaces are obtained. We make no additional assumptions on the quasi-metric or the doubling measure. Hence, the results of this paper extend earlier related results to a more general setting.

scholarly journals Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels

1994 ◽  
Vol 1 (1) ◽  
pp. 9-29
Author(s):  
I. Genebashvili ◽  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Weak Type ◽  
Sufficient Conditions ◽  
Nonnegative Function ◽  
Integral Transforms ◽  
Lorentz Spaces ◽  
Quasiconvex Functions ◽  
Homogeneous Type ◽  
Necessary And Sufficient ◽  
Positive Kernels ◽  
Homogeneous Type Space

Abstract Necessary and sufficient conditions are derived in order that an inequality of the form be fulfilled for some positive c independent of λ and a ν-measurable nonnegative function ƒ : X → R 1, where k : X × X × [0, ∞) → R 1 is a nonnegative measurable kernel, (X, d, μ) is a homogeneous type space, φη and ψ are quasiconvex functions, ψ ∈ Δ2, and t –α θ(t) is a decreasing function for some α, 0 < α < 1. A similar problem was solved in Lorentz spaces with weights.

scholarly journals Bounded Reasoning and Higher-Order Uncertainty

2021 ◽  
Author(s):  
Willemien Kets
Keyword(s):  
Game Theory ◽  
Finite Depth ◽  
Higher Order ◽  
Standard Assumption ◽  
Infinite Depth ◽  
Type Space ◽  
Classic Result ◽  
Type Spaces ◽  
Space Formalism ◽  
Bounded Reasoning

A standard assumption in game theory is that players have an infinite depth of reasoning: they think about what others think and about what others think that othersthink, and so on, ad infinitum. However, in practice, players may have a finite depth of reasoning. For example, a player may reason about what other players think, but not about what others think he thinks. This paper proposes a class of type spaces that generalizes the type space formalism due to Harsanyi (1967) so that it can model players with an arbitrary depth of reasoning. I show that the type space formalism does not impose any restrictions on the belief hierarchies that can be modeled, thus generalizing the classic result of Mertens and Zamir (1985). However, there is no universal type space that contains all type spaces.

scholarly journals Commutators on Weighted Morrey Spaces on Spaces of Homogeneous Type

2020 ◽  
Vol 8 (1) ◽  
pp. 305-334
Author(s):  
Ruming Gong ◽  
Ji Li ◽  
Elodie Pozzi ◽  
Manasa N. Vempati
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Doubling Measure ◽  
Bmo Space ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces

Abstract In this paper, we study the boundedness and compactness of the commutator of Calderón– Zygmund operators T on spaces of homogeneous type (X, d, µ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space L ω p , k ( X ) L_\omega ^{p,k}\left( X \right) with κ ∈ (0, 1) and ω ∈ Ap (X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure µ.

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