Notes on Bi-parameter Paraproducts

2025/11/04 by Shaabani, Shahaboddin
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2511.02789

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

In this note, we investigate the sharpness of existing bounds for various types of bi-parameter paraproducts acting between product Hardy spaces in the dyadic setting. We show that these bounds are sharp in most cases but fail to be so in one particular instance.

Citations

• Optimization algorithms for Carleson and sparse collections of sets
• The Operator Norm of Paraproducts on Bi-parameter Hardy spaces
• The Operator Norm of Paraproducts on Hardy Spaces
• Weighted L^p→ L^q-boundedness of commutators and paraproducts in the Bloom setting
• The L^p-to-L^q boundedness of commutators with applications to the Jacobian operator
• Equivalence of sparse and Carleson coefficients for general sets
• Multi-parameter paraproducts
• The Marcinkiewicz multiplier condition for bilinear operators

Related

• The Operator Norm of Paraproducts on Bi-parameter Hardy spaces
• Boundedness of a composition of dyadic paraproducts
• A T(b) Theorem on Product Spaces
• Logarithmic mean oscillation on the polydisc, endpoint results for\n multi-parameter paraproducts, and commutators on BMO
• Operator-valued dyadic BMO spaces