Two-weight Norm Estimates for Multilinear Fractional Integrals in\n Classical Lebesgue Spaces

2014/07/30 by Vakhtang Kokilashvili, Kokilashvili, Vakhtang, Mieczysław Mastyło +3
Mathematics · #42B25 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1407.8197

openalex publication_date 2014/07/30 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We derive criteria governing two-weight estimates for multilinear fractional\nintegrals and appropriate maximal functions. The two and one weight problems\nfor multi(sub)linear strong fractional maximal operators are also studied; in\nparticular, we derive necessary and sufficient conditions guaranteeing the\ntrace type inequality for this operator. We also establish the Fefferman-Stein\ntype inequality, and obtain one-weight criteria when a weight function is of\nproduct type. As a consequence, appropriate results for multilinear Riesz\npotential operator with product kernels follow.\n

Citations

• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

Related

• Two-weighted estimates of the multilinear fractional integral operator between weighted Lebesgue and Lipschitz spaces with optimal parameters
• Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators
• Two-weight inequalities for multilinear maximal functions in Orlicz spaces
• Two-weight inequalities for multilinear maximal functions in Orlicz spaces
• Optimal parameters related with continuity properties of the multilinear fractional integral operator between Lebesgue and Lipschitz spaces