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- Title
The ρ-variation of the Hermitian Riesz transform.
- Authors
Crescimbeni, Raquel; Martín-Reyes, Francisco; Torre, Alberto; Torrea, José
- Abstract
In this paper we prove the behaviour in weighted L spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps L(ℝ, w( x) dx) into itself when w is a weight in the A class for 1 < p < ∞. For p = 1 we get weak type for the A class. Weighted estimated are also obtained in the extreme case p = ∞.
- Subjects
INTEGRAL transforms; OSCILLATION theory of differential equations; NUMERICAL solutions to integral equations; HILBERT-Huang transform; OSCILLATIONS; ERGODIC theory
- Publication
Acta Mathematica Sinica, 2010, Vol 26, Issue 10, p1827
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-010-9122-3