Regular orthogonal basis on Heisenberg group and application to function spaces

Abstract

In this paper, we construct some compactly supported orthogonal regular wavelet basis on Heisenberg group H d . Because of the regularity of wavelets, we could use such wavelets to characterize function spaces on H d , such as bounded mean oscillation space (BMO) space, Hardy space, Besov spaces and Besov-Morrey spaces.where S.z, z 0 / D 2Q szN z 0 is the symplectic inner product (or symplectic form). Alternatively, by the real coordinates, the aforementioned multiplication can be represented as .x, y, t/.x 0 , y 0 , t 0 / D .x C x 0 , y C y 0 , t C t 0 C 2.y 0 x x 0 y//, (2.2)

Extension of Q‐type spaces related with weight functions via convolution operators on Heisenberg groups

“…The following wavelet characterization of $$$ BMO\left({\mathbb{H}}^n\right) $$$ is obtained by Yang and Li 29 …”