Abstract. In this work we investigate the construction of Carleson measures from families of multilinear integral operators applied to tuples of L∞ and BMO functions. We show that if the family Rt of multilinear operators possesses cancellation in each variable, then for BMO functions b1, . . . , bm, the measure |Rt(b1, . . . , bm)(x)|dxdt/t is Carleson. However, if the family of multilinear op...

In this paper we study Carleson and reverse measures for holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions sufficient in order measure $$\mu $$ to be mixed-normed weighted Bergman spaces.

We investigate a variant of the Beurling-Ahlfors extension quasisymmetric homeomorphisms real line that is given by convolution heat kernel, and prove complex dilatation such quasiconformal strongly symmetric homeomorphism (i.e. its derivative an ${\rm A}_\infty$-weight whose logarithm in VMO) induces vanishing Carleson measure on upper half-plane.

For α > 0 , several characterizations of the id="M2"> -Bloch spaces harmonic mappings are given. We also obtain similar for closed separable subspace. As an application, we give relations between id="M3"> B H and Carleson’s me...

We prove that when subjected to periodic forcing of the form pμ,ρ,ω(t) = μ(ρh(x, y) + sin(ωt)), certain second order systems of differential equations with dissipative homoclinic loops admit strange attractors with SRB measures for a set of forcing parameters (μ, ρ, ω) of positive measure. Our proof applies the recent theory of rank one maps, developed by Wang and Young [30, 34] based on the an...

An alternative interpretation of a family of weighted Carleson measures is used to characterize p-Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic functi...