Weighted L estimates for the Bergman and Szegő projections on strongly pseudoconvex domains with near minimal smoothness

Weighted endpoint bounds for the Bergman and Cauchy-Szegő projections on domains with near minimal smoothness

“…In fact, Theorem 1.1 and an interpolation argument imply the L p (D), 1 < p < ∞, boundedness result of [11] in the case of D having C 4 boundary. With B 1 weights, Theorem 1.1 generalizes Bekollé's endpoint weak-type result of [1] to domains with near minimal smoothness and extends the work in [18] to address the p = 1 endpoint.…”

“…The above result for 1 < p < ∞ was recently extended to the near minimal smoothness case where D is a strongly pseudoconvex bounded domain with C 4 boundary by the second author and Wick in [18]. In Section 2, we use the same condition for B 1 weights with respect to the quasi-metric defined therein.…”

“…The bounds of S on L p σ (bD) for 1 < p < ∞ and σ ∈ A p were recently established in the near minimal smoothness case where D is a strongly pseudoconvex bounded domain with C 3 boundary by the second author and Wick in [18].…”

Weighted theory of Toeplitz operators on the Bergman space

“…If [σ] Bp < ∞, we write σ ∈ B p and refer to [σ] Bp as the Békollè-Bonami characteristic of σ. We refer to [20,21,28,35] for recent weighted L p σ theory of P and to [32] for recent weighted endpoint weak-type theory of P .…”

“…Theorem A has been extended to strongly pseudoconvex domains with smooth boundary by Wang and Xia in [36]. The sufficiency direction of Theorem B has been extended for p > 1 to simple domains by Huo, Wick, and the second author in [20,21] and to strongly pseudoconvex domains with C 4 boundary by Wick and the second author in [35]; this direction of Theorem B when p = 1 has been extended to strongly pseudoconvex domains with C 4 boundary by the authors in [32] and should hold for simple domains following ideas from [25].…”