Cesàro operator induced by a Bergman kernel

@misc{blasco2026cesàro,
  title = {{Cesàro operator induced by a Bergman kernel}},
  author = {Oscar Blasco and Atte Pennanen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21657},
  eprint = {2609.21657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21657},
}

TY  - UNPB
TI  - Cesàro operator induced by a Bergman kernel
AU  - Oscar Blasco
AU  - Atte Pennanen
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21657
UR  - https://arxiv.org/abs/2609.21657
AB  - Let μ be a positive Borel measure on [0,1) and ω a radial weight. In this paper we consider the Cesàro-type operator C_μ,ω induced by the reproducing kernel B^ω of the weighted Bergman space A^2_ω, given by C_μ,ω(f)(z)=∫_0^1f(tz)B^ω_t(z) dμ(t), z ∈ 𝔻, for functions f analytic in 𝔻. Under the assumption that ω satisfies a natural doubling property, we study the boundedness of C_μ,ω acting on several spaces of analytic functions, including Hardy spaces H^p and weighted Bergman spaces A^p_ν. For 0<p,q<∞ and a two-sided doubling weight ν, we completely characterize when C_μ,ω: H^p → H^q and C_μ,ω: A^p_ν → A^q_ν are bounded in terms of the interplay of tail integrals or moments of the inducing weights and the measure μ. Many of the results obtained are new even in the setting of standard weights or when the Bergman reproducing kernel is replaced by the Cauchy kernel. In addition, we consider C_μ,ω acting on H^∞, Korenblum spaces and weighted Hardy spaces.
ER  -