1998/10/01 by Nicola Arcozzi · 33 citations
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #Advanced Banach Space Theory #Lie group #Mathematics #Gauss #SPHERES #Space (punctuation) #Riesz transform #Pure mathematics #Physics #Linguistics #Astronomy #Quantum mechanics #Philosophy
paper · pdf · doi:10.1007/bf02384766
published in Arkiv för matematik 36(2), 201-231 (Mittag-Leffler Institute)
openalex publication_date 1998/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Riesz transforms on compact Lie groups, spheres and Gauss spaceNicola Arcozzi(x) Notation.For x, yER ~, x=(xl,...,x~), Y=(Yl,...,Y~), Ixl=(EjLlx~) 1/2 is n the Euclidean norm of x and (x, y:~j 0 xjyj is the inner product of x and y.Sometimes, we write x.y instead of (x, y.If (X, Jr, #) is a measure space, f: X~R n is a measurable function and pe[1, oc), the L p norm of f is defined by Ilfllp=functions on (X, hC,#) to R "~ valued n p functions on (X1,~c1,#1), that IISIIp= supllSfllp: II/llp=l is the operator norm of S. If X=X1 and #=#1, we denote by I| the operator with (I| S f), the latter being an R ~+'~ valued function.Let ,4 be a linear space of integrable functions on (X, 9 r, #).We denote by A0 the subspace Ao =IEA:fx f d#=0.If a linear operator S is only defined on A0, we still denote by IISIIp=supllSfllp:feAo, [l/lip=l.For instance, C~(M)=Ic c ~(M):/. f(x)d~=0, if M is a smooth aiemannian manifold and dx denotes thevolume element on M. The L p norm of a measurable vector field U on M is, by definition, the Lp norm of IU], the modulus of U. Unless otherwise specified, LP(X) and L~(X) will denote spaces of real valued fimetions on X.