The boundedness of sublinear operators on Morrey-Herz spaces over the homogeneous type space

2013 ◽  
Vol 39 (1) ◽  
pp. 69-85 ◽  
Author(s):  
Yanlong Shi ◽  
Xiangxing Tao
Keyword(s):  
Homogeneous Type ◽  
Herz Spaces ◽  
Type Space ◽  
Sublinear Operators ◽  
Homogeneous Type Space

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 Boundedness of some sublinear operators on Herz spaces

1996 ◽  
Vol 40 (3) ◽  
pp. 484-501 ◽  
Author(s):  
Xinwei Li ◽  
Dachun Yang
Keyword(s):  
Herz Spaces ◽  
Sublinear Operators

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 Two weight estimates for a class of (p, q) type sublinear operators and their commutators

2019 ◽  
Vol 17 (1) ◽  
pp. 758-775 ◽  
Author(s):  
Hu Yunpeng ◽  
Zhou Jiang ◽  
Cao Yonghui
Keyword(s):  
Norm Inequalities ◽  
Type Space ◽  
Sublinear Operators ◽  
Amalgam Spaces

Abstract In the present paper, the authors investigate the two weight, weak-(p, q) type norm inequalities for a class of sublinear operators 𝓣γ and their commutators [b, 𝓣γ] on weighted Morrey and Amalgam spaces. What should be stressed is that we introduce the new BMO type space and our results generalize known results before.

scholarly journals A note on the boundedness of sublinear operators on grand variable Herz spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hammad Nafis ◽  
Humberto Rafeiro ◽  
Muhammad Asad Zaighum
Keyword(s):  
Herz Spaces ◽  
Sublinear Operators ◽  
Type Spaces

AbstractIn this paper, we introduce grand variable Herz type spaces using discrete grand spaces and prove the boundedness of sublinear operators on these spaces.

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