Two weight norm inequalities for the bilinear fractional integrals

Abstract

In this paper, we give a characterization of the two weight strong and weak type norm inequalities for the bilinear fractional integrals. Namely, we give the characterization of the following inequalities, \[ \|\mathcal I_α(f_1σ_1, f_2σ_2)\|_{L^q(w)} \le \mathscr N \prod_{i=1}^2\|f_i\|_{L^{p_i}(σ_i)} \] and \[ \|\mathcal I_α(f_1σ_1, f_2σ_2)\|_{L^{q,\infty}(w)} \le \mathscr N_{\textup{weak}} \prod_{i=1}^2\|f_i\|_{L^{p_i}(σ_i)}, \] when $q\ge p_1,p_2>1$ and $p_1+p_2\ge p_1{p}_2$.

16 pages

References in corpus (3)

• Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, II
• Two weight estimate for the Hilbert transform and corona decomposition for non-doubling measures
• Characterization of a Two Weight Inequality for Multilinear Fractional Maximal Operators