Oscillation and variation for Riesz transform in setting of Bessel operators on H1 and BMO

2020 ◽  
Vol 15 (4) ◽  
pp. 617-647
Author(s):  
Xiaona Cui ◽  
Jing Zhang
Keyword(s):  
Riesz Transform ◽  
Bessel Operators

scholarly journals Compactness of Riesz transform commutator associated with Bessel operators

2018 ◽  
Vol 135 (2) ◽  
pp. 639-673 ◽  
Author(s):  
Xuan Thinh Duong ◽  
Ji Li ◽  
Suzhen Mao ◽  
Huoxiong Wu ◽  
Dongyong Yang
Keyword(s):  
Riesz Transform ◽  
Bessel Operators

scholarly journals Oscillation and variation for the Riesz transform associated with Bessel operators

2018 ◽  
Vol 149 (1) ◽  
pp. 169-190 ◽  
Author(s):  
Huoxiong Wu ◽  
Dongyong Yang ◽  
Jing Zhang
Keyword(s):  
Riesz Transform ◽  
Bessel Operator ◽  
Bessel Operators ◽  
Variation Operator ◽  
Image Position ◽  
Oscillation Operator

Let λ > 0 and letbe the Bessel operator on ℝ+ := (0,∞). We show that the oscillation operator 𝒪(RΔλ,∗) and variation operator 𝒱ρ(RΔλ,∗) of the Riesz transform RΔλ associated with Δλ are both bounded on Lp(ℝ+, dmλ) for p ∈ (1,∞), from L1(ℝ+, dmλ) to L1,∞(ℝ+, dmλ), and from L∞(ℝ+, dmλ) to BMO(ℝ+, dmλ), where ρ ∈ (2,∞) and dmλ(x) := x2λ dx. As an application, we give the corresponding Lp-estimates for β-jump operators and the number of up-crossings.

Riesz transform and g-function associated with Bessel operators and their appropriate Banach spaces

2007 ◽  
Vol 157 (1) ◽  
pp. 259-282 ◽  
Author(s):  
Jorge J. Betancor ◽  
Juan Carlos Fariña ◽  
Teresa Martínez ◽  
José Luis Torrea
Keyword(s):  
Banach Spaces ◽  
Riesz Transform ◽  
Bessel Operators

scholarly journals REAL-VARIABLE CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BESSEL OPERATORS

2011 ◽  
Vol 09 (03) ◽  
pp. 345-368 ◽  
Author(s):  
DACHUN YANG ◽  
DONGYONG YANG
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Real Variable ◽  
Bessel Operator ◽  
Bessel Operators ◽  
Lusin Area Function ◽  
Radial Maximal Function ◽  
Nontangential Maximal Function

Let λ > 0, p ∈ ((2λ + 1)/(2λ + 2), 1], and [Formula: see text] be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces Hp((0,∞),dmλ) associated with △λ in terms of the radial maximal function, the nontangential maximal function, the grand maximal function, the Littlewood–Paley g-function and the Lusin-area function, where dmλ(x) ≡ x2λ dx. As an application, the authors further obtain the Riesz transform characterization of these Hardy spaces.

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

2021 ◽  
pp. 1-37
Author(s):  
Martijn Caspers
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Riesz Transform ◽  
Wreath Products ◽  
Compact Quantum Group ◽  
Riesz Transforms ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Free Products ◽  
Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

scholarly journals The Higher Order Riesz Transform andBMOType Space Associated with Schrödinger Operators on Stratified Lie Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yu Liu ◽  
Jianfeng Dong
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Riesz Transform ◽  
Integral Operators ◽  
Higher Order ◽  
Reverse Hölder Class ◽  
Stratified Lie Group ◽  
Homogeneous Dimension ◽  
Stratified Lie Groups ◽  
Reverse Hölder

Assume thatGis a stratified Lie group andQis the homogeneous dimension ofG. Let-Δbe the sub-Laplacian onGandW≢0a nonnegative potential belonging to certain reverse Hölder classBsfors≥Q/2. LetL=-Δ+Wbe a Schrödinger operator on the stratified Lie groupG. In this paper, we prove the boundedness of some integral operators related toL, such asL-1∇2,L-1W, andL-1(-Δ) on the spaceBMOL(G).

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