Riesz transforms and multipliers for the Grushin operator
نویسندگان
چکیده
منابع مشابه
On the Grushin Operator and Hyperbolic Symmetry
Complexity of geometric symmetry for differential operators with mixed homogeniety is examined here. Sharp Sobolev estimates are calculated for the Grushin operator in low dimensions using hyperbolic symmetry and conformal geometry. Considerable interest exists in understanding differential operators with mixed homogeneity. A simple example is the Grushin operator on R ∆G = ∂ ∂t2 + 4t ∂ ∂x2 . T...
متن کاملBessel, Frame and Riesz Multipliers
Abstract. This paper introduces the concept of Bessel and frame multipliers. These operators are defined by a fixed pattern, called the symbol, which is used after analysis, before synthesis. This concept is a generalization of Gabor multipliers. It allows specialization to any analysis/synthesis systems, that form Bessel sequences, like e.g. wavelet frames. Basic properties of this general cla...
متن کاملIndefinite higher Riesz transforms
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 کاملPrincipal Values for Riesz Transforms and Rectifiability
Let E ⊂ R with H(E) < ∞, where H stands for the n-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit
متن کاملANALYSIS CLUB Bochner-Riesz Multipliers
We now consider the family of operators Tλ, λ ≥ 0, defined on Rn by T̂λ f (ξ) = mλ f̂ (ξ), where mλ(ξ) = (1− |ξ|)+. These are the Bochner-Riesz multipliers, which can be viewed as an attempt to smooth out the singularity of the disc multiplier to see if we can obtain boundedness on a wider range of Lp spaces. Note that when λ = 0 we obtain S1, and that as λ increases, the multiplier mλ becomes sm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2013
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-013-0008-z