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𝒩(p, q, s)-type spaces in the unit ball of ℂn(II): Carleson measure and its application

  • Bingyang Hu and Songxiao Li EMAIL logo
Published/Copyright: September 11, 2019
Forum Mathematicum
From the journal Forum Mathematicum Volume 32 Issue 1

Abstract

The purpose of this paper is to study a new class of function spaces, called 𝒩⁢(p,q,s)-type spaces, in the unit ball 𝔹 of ℂn. The Carleson measure on such spaces is investigated. Some embedding theorems among 𝒩⁢(p,q,s)-type spaces, weighted Bergman spaces and weighted Hardy spaces are established. As for applications, the Hadamard products and random power series on 𝒩⁢(p,q,s)-type spaces are also studied.

Keywords: weighted Bergman spaces; weighted Hardy spaces; Hadamard product; random power series
MSC 2010: 32A36; 47B38; 32A05

Communicated by Christopher D. Sogge

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11720101003

Funding statement: The corresponding author was supported by the Macao Science and Technology Development Fund (No.186/2017/A3) and NNSF of China (No. 11720101003).

Acknowledgements

The authors thank the referee for his(or her) several helpful remarks and comments that led to the improvement of this paper.

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Received: 2019-07-05
Revised: 2019-07-30
Published Online: 2019-09-11
Published in Print: 2020-01-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. On the distribution of zeros of derivatives of the Riemann ξ-function
  3. Representations of constant socle rank for the Kronecker algebra
  4. Abstract bivariant Cuntz semigroups II
  5. Curves on Segre threefolds
  6. 𝒩(p, q, s)-type spaces in the unit ball of ℂn(II): Carleson measure and its application
  7. On a class of critical Robin problems
  8. On the description of multidimensional normal Hausdorff operators on Lebesgue spaces
  9. Spectral asymptotics for Krein–Feller operators with respect to 𝑉-variable Cantor measures
  10. Schneider–Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits
  11. Modified energy method and applications for the well-posedness for the higher-order Benjamin–Ono equation and the higher-order intermediate long wave equation
  12. Some remarks on products of sets in the Heisenberg group and in the affine group
  13. Codimension growth of central polynomials of Lie algebras
  14. Unramified Whittaker functions for certain Brylinski–Deligne covering groups
  15. Tilting classes over commutative rings
https://doi.org/10.1515/forum-2019-0174
Keywords for this article
weighted Bergman spaces; weighted Hardy spaces; Hadamard product; random power series

Articles in the same Issue

  1. Frontmatter
  2. On the distribution of zeros of derivatives of the Riemann ξ-function
  3. Representations of constant socle rank for the Kronecker algebra
  4. Abstract bivariant Cuntz semigroups II
  5. Curves on Segre threefolds
  6. 𝒩(p, q, s)-type spaces in the unit ball of ℂn(II): Carleson measure and its application
  7. On a class of critical Robin problems
  8. On the description of multidimensional normal Hausdorff operators on Lebesgue spaces
  9. Spectral asymptotics for Krein–Feller operators with respect to 𝑉-variable Cantor measures
  10. Schneider–Siegel theorem for a family of values of a harmonic weak Maass form at Hecke orbits
  11. Modified energy method and applications for the well-posedness for the higher-order Benjamin–Ono equation and the higher-order intermediate long wave equation
  12. Some remarks on products of sets in the Heisenberg group and in the affine group
  13. Codimension growth of central polynomials of Lie algebras
  14. Unramified Whittaker functions for certain Brylinski–Deligne covering groups
  15. Tilting classes over commutative rings
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