Oscillating multipliers on the Heisenberg group

• Autorzy: E. K. Narayanan , S. Thangavelu
• Języki publikacji: EN

Abstrakty

EN

Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{-1/2} sin√ℒ$ is bounded on $L^{p}(Hⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.

Kategorie tematyczne

• 43A80: Analysis on other specific Lie groups
• 22E30: Analysis on real and complex Lie groups
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 90
• Numer: 1
• Strony: 37-50

Daty

wydano

2001

Twórcy

autor

E. K. Narayanan

• Statistics and Mathematics Division, Indian Statistical Institute, 8th mile Mysore Road, Bangalore 560 059, India

autor

S. Thangavelu

• Statistics and Mathematics Division, Indian Statistical Institute, 8th mile Mysore Road, Bangalore 560 059, India

Identyfikatory

DOI

10.4064/cm90-1-3