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bessel operator

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Oscillation and variation for the Riesz transform associated with Bessel operators
Part of
- Harmonic analysis in several variables
Huoxiong Wu, Dongyong Yang, Jing Zhang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 1 / February 2019

Published online by Cambridge University Press:

18 September 2018, pp. 169-190

Print publication:

February 2019
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Let λ > 0 and let
be 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.