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 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.

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.

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