A "deformation estimate" for the Toeplitz operators on harmonic Bergman spaces

作者：Liu Congwen^*

来源：Proceedings of the American Mathematical Society, 2007, 135(9): 2867-2876.

DOI：10.1090/S0002-9939-07-08800-4

• Toeplitz operators
• harmonic bergman spaces
• deformation estimate
• Berezin type transforms

Let B denote the open unit ball in R-n for n >= 2 and dx the Lebesgue volume measure on R-n. For alpha >= -1, the ( weighted) harmonic Bergman space b(2,alpha)(B) is the space of all harmonic functions u which are in L-2(B, (1- vertical bar x vertical bar(2))(alpha)dx). For f. is an element of L-infinity (B), the Toeplitz operator T-f((alpha)) f is decreased on b(2,alpha) (B) by T-f((alpha)) u = Q(alpha)[f u], where Q(alpha) is the orthogonal projection of L-2 (B, (1- vertical bar x vertical bar(2))(alpha)dx) onto b(2,alpha) (B). In this note, we prove that for f is an element of C (B) boolean AND L-infinity (B) radial, lim(alpha-infinity) vertical bar vertical bar T-f((alpha))vertical bar vertical bar = vertical bar vertical bar f vertical bar vertical bar(infinity).

• 出版日期2007
• 单位中国科学技术大学