H(⊗1 C+) denotes the Hardy space of square integrable functions analytic in each variable separately. Let P be the natural projection of L(⊗1 C+) onto H (⊗1 C+). A Hankel operator with symbol b is the linear operator from H(⊗1 C+) to H (⊗1 C+) given by Hb φ = P⊖bφ. We show that ‖Hb‖ ≃ ‖P b‖BMO(⊗n 1 C+) , where the right hand norm is S.-Y. Chang and R. Fefferman product BMO. This fact has well k...

Let X be a doubling metric measure space. In this paper, the authors introduce the notions of Property (M̃) and Property (P ) of X , prove that Property (M̃) implies Property (P ) and give some equivalent characterizations of Property (M̃) and Property (P ). If X has Property (P ), the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the se...

Several spaces defined according to different formulations for operator-valued functions in BMO are defined and studied.

Adsorption is a low-energy, economical, and efficient method for pollutant removal from water. Because of their unique structure, large specific surface area (SSA), non-toxicity, bismuth-based semiconductors, usually researched the photodegradation organic molecules, are also excellent dark adsorption processes. Here, three-dimensional adsorbent with heterostructure hydrangea-like shape made Bi...

In this work we prove Hardy space estimates for bilinear Littlewood-Paley-Stein square function and Calderón-Zygmund operators. Sufficient Carleson measure type conditions are given for square functions to be bounded from H p1 ×H p2 into Lp for indices smaller than 1, and sufficient BMO type conditions are given for a bilinear Calderón-Zygmund operator to be bounded from H p1 ×H p2 into H p for...

Abstract We introduce a space of $$L^2$$ L 2 vector fields with bounded mean oscillation whose “normal” component to the boundary is well-controlled. establish its Helmholtz decomposition in case when domain perturbed $$C^3$$ C 3 half $...

We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the leading coefficients are measurable in one variable and have small BMO semi-norms in the other variables, variable exponents p(x) satisfy log-Hölder continuity, and the boundarie...

Starting with the relatively simple observation that variational estimates of commutators standard Calderón-Zygmund operators bounded mean oscillation (BMO) functions can be obtained from their weighted estimates, we establish similar for BMO rough singular integrals, which do not admit any estimates. The proof involves several Littlewood-Paley-type inequalities as well Bony decomposition and r...