Absolutely summing Carleson embeddings on weighted Fock spaces with A_∞-type weights

2025/05/22 by Jiale Chen, Bo He, Chen, Jiale +3 · 2 citations
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2505.16109

Abstract

In this paper, we investigate the r-summing Carleson embeddings on weighted Fock spaces F^p_α,w. By using duality arguments, translating techniques and block diagonal operator skills, we completely characterize the r-summability of the natural embeddings I_d:F^p_α,w→ L^p_α(μ) for any r≥1 and p>1, where w is a weight on the complex plane ℂ that satisfies an A_p-type condition. As applications, we establish some results on the r-summability of differentiation and integration operators, Volterra-type operators and composition operators. Especially, we completely characterize the boundedness of Volterra-type operators and composition operators on vector-valued Fock spaces for all 1

Cited by

• Toeplitz operators on weighted Fock spaces with A_∞-type weights
• Absolutely Summing Toeplitz operators on Fock spaces

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