Erratum to: Martingale transforms and $$L^p$$ L p -norm estimates of Riesz transforms on complete Riemannian manifolds
نویسندگان
چکیده
منابع مشابه
TWO-SIDED Lp ESTIMATES OF CONVOLUTION TRANSFORMS
where ψ{v) = u, u. R. O'Neil obtained sharp upper and lower estimates when ψ(u) — u and n — 2, [3, Lemma 1.5]. Our results coincide with his for this case. We were able to apply our estimates for the case ψ(u) = u (^-arbitrary) to classical Fourier transform inequalities of Hardy and Little wood. The main problem of this paper is to determine whether or not one can obtain the same types of uppe...
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We prove Lp-bounds for the Riesz transforms d/ √ −∆, δ/ √ −∆ associated with the Hodge-Laplacian ∆ = −δd − dδ equipped with absolute and relative boundary conditions in a Lipschitz subdomain Ω of a (smooth) Riemannian manifoldM, for p in a certain interval depending on the Lipschitz character of the domain.
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On the Euclidean space, it is well known that the Riesz transform has also a bounded extension L(M) → L(M ;TM) for any p ∈]1,∞[. However, this is not a general feature of the Riesz transform on complete Riemannian manifolds, as the matter of fact, on the connected sum of two copies of the Euclidean space R , the Riesz transform is not bounded on L for any p ∈ [n,∞[∩]2,∞[ ([9, 7]). It is of inte...
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Stein’s higher Riesz transforms are translation invariant operators on L2(Rn) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete series representations for hyperboloids associated to the indefini...
متن کاملNon - Commutative Martingale Transforms
We prove that non-commutative martingale transforms are of weak type (1, 1). More precisely, there is an absolute constant C such that if M is a semi-finite von Neumann algebra and (Mn)n=1 is an increasing filtration of von Neumann subalgebras of M then for any non-commutative martingale x = (xn) ∞ n=1 in L 1(M), adapted to (Mn)n=1, and any sequence of signs (εn) ∞ n=1, ∥∥∥∥ε1x1 + N ∑ n=2 εn(xn...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2014
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-014-0560-1