On regularity of twisted spherical means and special Hermite expansions

Proceedings - Mathematical Sciences - Tập 103 - Trang 303-320 - 1993
S Thangavelu1
1TIFR Centre, Bangalore, India

Tóm tắt

Regularity properties of twisted spherical means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As an application we prove a localisation theorem for special Hermite expansions.

Tài liệu tham khảo

Colzani L, Regularity of spherical means and localisation of spherical harmonic expansions,J. Austr. Math. Soc. 41 (1986) 287–297 Folland G, Harmonic analysis in phase space Ann. Math. Stud. (Princeton: University Press) 112 (1989) Mauceri G, Picardello M and Ricci F, A Hardy space associated with twisted convolution,Adv. Math. 39 (1981) 270–288 Oberlin D and Stein E, Mapping properties of the Radon transform,Indiana Univ. Math. J. 31 (1982) 641–650 Pinsky M A, Spectral analysis of the Laplacian on piecewise smooth functions (preprint) Peetre J and Sparr G, Interpolation and non-commutative integration,Ann. Mat. Pura. Appl. Vol. CIV (1975) 187–207 Peyriere J and Sjolin P, Regularity of spherical means,Ark. Mat. 16 (1978) 177–126 Sjolin P, Norm inequalities for spherical means,Mh. Math. 100 (1985) 153–161 Stein E,Singular integrals and differentiability properties of functions (Princeton University Press) (1971) Stein E, Maximal functions: spherical means,Proc. Natl. Acad. Sci. USA 73 (1976) 2174–2175 Strichartz R, Harmonic analysis as spectral theory of Laplacians,J. Funct. Anal. 87 (1989) 51–148 Szego G, Orthogonal polynomials,Am. Math. Soc. Colloq. Pub., (Providence: Am. Math. Soc.) (1967) Thangavelu S, On almost everywhere and mean convergence of Hermite and Laguerre expansions,Colloq. Math. 60 (1990) 21–34 Thangavelu S, Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform,Revist. Mat. Ibero. (1991) vol.7, No. 2 (1991) 135–155 Thangavelu S, On conjugate poisson integrals and Riesz transforms for the Hermite expansions,Colloq. Math. vol.LXIV (1993) 103–113 Thangavelu S,Lectures on Hermite and Laguerre expansions Math. Notes No. 42 (Princeton: University Press) (to appear)