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Research Article Open access CC BY 4.0

Application on a Factor Derived from Hilbert and Carleson Measure on Hardy Spaces

Amani Elseid Abuzeid

Journal of Advances in Mathematics and Computer Science · pp. 47–66 · Published 22 Apr 2023

10.9734/jamcs/2023/v38i71771

Abstract

For \(\mu_j\) to a positive Borel measure on the interval \([0,1)\). The Hankel matrix \(\mathcal{H}_{\mu_j}=\left(\left(\mu_j\right)_{n, k}\right)_{j, n, k \geq 0}\) with entries \(\left(\mu_j\right)_{n, k}=\left(\mu_j\right)_{n+k}\), where \(\left(\mu_j\right)_n=\int_{[0,1)} t^n d \mu_j(t)\), the operator is formally induced \[ \sum_i \mathcal{D} \mathcal{H}_{\mu_j}\left(f_j\right)(z)=\sum_{n=0}^{\infty} \sum_{k=0}^{\infty} \sum_i\left(\left(\mu_j\right)_{n, k} a_k\right)(n+1) z^n \] in the space of each analytical function \(f_j(z)=\sum_{k=0}^{\infty} a_k z_n\) in the unit disc \(\mathbb{D}\). We classify positive Borel measures on [0,1) as such \(\mathcal{D} \mathcal{H}_{\mu_j}\left(f_j\right)(z)=\int_{[0,1)} \frac{f_j(t)}{(1-t z)^2} d \mu_j(t)\) for all in Hardy spaces \(H^{1+\epsilon}(0 \leq \epsilon<\infty)\), and we describe those for which \(\mathcal{D} \mathcal{H}_{\mu_j}\) is a bounded* operator from \(H^{1+\epsilon}(0 \leq \epsilon<\infty)\) into \(H^{1+2 \epsilon}(\epsilon \geq 0)\).

Hardy spaces carleson measure derivative hilbert operator

References (14)

  1. 1 Operator Theory in Function Spaces [DOI]
  2. 2 On Bloch functions and normal functions. [DOI]
  3. 3 Composition operators and the Hilbert matrix [DOI]
  4. 4 A generalized Hilbert matrix acting on Hardy spaces [DOI]
  5. 5 A Hankel matrix acting on Hardy and Bergman spaces [DOI]
  6. 6 Generalized Hilbert operators [DOI]
  7. 7 A Derivative-Hilbert Operator Acting on the Bloch Space [DOI]
  8. 8 A Derivative-Hilbert operator acting on Bergman spaces [DOI]
  9. 9 A Carleson Measure Theorem for Bergman Spaces [DOI]
  10. 10 Vanishing logarithmic Carleson measures [DOI]
  11. 11 On Bloch functions and gap series. [DOI]
  12. 12 Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space [DOI]
  13. 13 A Derivative-Hilbert operator acting on Hardy spaces [DOI]
  14. 14 Composition Operators on Spaces of Analytic Functions [DOI]

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