Spaces of Goldberg type on certain measured metric spaces

作者：Meda Stefano^*; Volpi Sara

来源：Annali di Matematica Pura ed Applicata, 2017, 196(3): 947-981.

DOI：10.1007/s10231-016-0603-6

• Local Hardy space
• Atom
• Goldberg-type space
• Riesz transform

In this paper, we define a space h(1)(M) of HardyGoldberg type on a measured metric space satisfying some mild conditions. We prove that the dual of h(1)(M) may be identified with bmo(M), a space of functions with local bounded mean oscillation, and that if p is in (1, 2), then L-p(M) is a complex interpolation space between h(1)(M) and L-2(M). This extends previous results of Strichartz, Carbonaro, Mauceri and Meda, and Taylor. Applications to singular integral operators on Riemannian manifolds are given.

• 出版日期2017-6