In this paper, we study the Bergman kernel Bφ(x,y) of generalized Bargmann-Fock spaces in setting Clifford algebra. The versions L2-estimate method and weighted subharmonic inequality for algebra are established. Consequently show existence then give some estimates on- off- diagonal. As a by-product, also obtain an upper estimate harmonic kernel.

We prove that Bergman projections on weighted mixed norm spaces smoothly bounded domains in $\mathbb{R}^n$ are for a certain range of parameters such and assuming conditions weights. The proof relies estimates integral means $M_p(P_\gamma f, r)$ terms $f$. This result complements earlier boundedness $P_\gamma$ closely related space $L^{p,q}_\alpha(\Omega).$

In this paper we consider a class of weighted composition operators defined on the Bergman spaces L2a (dA?) where D is open unit disk in C and dA?(z) = (? + 1)(1 ? |z|2)?dA(z), > ?1 dA(z) area measure D. These are also self-adjoint unitary. We establish here that bounded linear operator S from into itself commutes with all C(?) , D, if only B?S satisfies certain averaging condition. Here den...

We apply the Bekollé–Bonami estimate for (positive) Bergman projection on weighted $$L^p$$ spaces unit disk. As consequences, we obtain boundedness of Sobolev space symmetrized bidisk. also improve result unweighted bidisk in Chen et al. (J Funct Anal 279(2):108522, 2020).