A Sharp Norm Estimate of the Bergman Projection on L Spaces

$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles

‎In this paper we investigate a two classes of domains in $mathbb{C}^n$ generalizing the Hartogs triangle‎. ‎We prove optimal estimates for the mapping properties of the Bergman projection on these domains.

A Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

Harmonic Bergman Functions on Half-spaces

We study harmonic Bergman functions on the upper half-space of Rn. Among our main results are: The Bergman projection is bounded for the range 1 < p <∞; certain nonorthogonal projections are bounded for the range 1 ≤ p < ∞; the dual space of the Bergman L1-space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range 1 ≤ p <∞; the Bergma...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Duality of Holomorphic Function Spaces and Smoothing Properties of the Bergman Projection

Let Ω ⊂⊂ C be a domain with smooth boundary, whose Bergman projection B maps the Sobolev space H1(Ω) (continuously) into H2(Ω). We establish two smoothing results: (i) the full Sobolev norm ‖Bf‖k2 is controlled by L derivatives of f taken along a single, distinguished direction (of order ≤ k1), and (ii) the projection of a conjugate holomorphic function in L(Ω) is automatically in H2(Ω). There ...