Integral operators with rough kernels in variable Lebesgue spaces

2019/09/20 by Marta Urciuolo, Urciuolo, Marta, Lucas Vallejos +1
Mathematics · #42B25 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42B25 #msc:42B35

paper · pdf · doi:10.48550/arxiv.1909.09322

arxiv created 2019/09/20 · arxiv updated 2019/09/23

Abstract

In this paper we study integral operators with kernels K(x,y)= k₁( x- A₁y)...k_m( x-A_my), k_i(x)=\fracΩ_i(x)|x|^n/q_i where Ω_i: ℝⁿ→ ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A_i are certain invertible matrices, and \frac nq₁+…\frac nq_m=n-α, 0≤ α<n. We obtain the boundedness of this operator from L^p(⋅) into % L^q(⋅) for (1)/(q(⋅))=(1)/(p(⋅))-(α)/(n), for certain exponent functions p satisfying weaker conditions than the classical log-Hölder conditions.

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