2016/01/21 by Nguyen Minh Chuong, Chuong, Nguyen Minh, Nguyễn Thị Thuý Hồng +6
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CA
paper · pdf · doi:10.48550/arxiv.1601.05542
arxiv created 2016/01/21 · openalex publication_date 2016/01/21 · arxiv updated 2016/01/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We obtain sufficient and necessary conditions on weight functions s1(t),…,sm(t) and ψ(t) so that the weighted multilinear Hardy-Cesàro operator (f1,…,fm)↦ ∫[0,1]n(∏k=1nfk(sk(t) x))ψ(t)dt is bounded from Kα1, p1q1(ω1)× ⋯ ×Kαm, pmqm(ωm) to Kα, pq(ω) and from MKα1, λ1p1,q1(ω1)× ⋯ × MKαm, λmpm,qm(ωm) to MKα, λp,q(ω). The sharp bounds are also obtained and these results hold for both cases 0<p<1 and 1≤ p<∞. We give a sufficient condition so that if symbols b1,…,bm are Lipschitz, then the commutator of the weighted Hardy-Cesàro operator (f1,…,fm)↦∫[0,1]n(∏k=1mfk(sk(t)x))(∏k=1m(bk(x)-bk(sk(t)x)))ψ(t)dt is bounded from MKα1, λ1p1, q1(ω1)× ⋯ × MKαm, λmpm, qm(ωm) to MKα^′, λp, q(ω) for both cases 0<p<1 and 1≤ p<∞. By these we extend and strengthen previous results deu to Tang, Xue, and Zhou [16].