The duality between Hl and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained . Using the atomic decomposition approach ([C], [L]) the author studied the problem of characterizing the dual space of Hl of vector-valued functions . In [B2] the author showed, for the case SZ = {Iz1 = 1}, tha...

Physiological and regulatory mechanisms that allow the alkane-oxidizing bacterium Pseudomonas butanovora to consume C2 to C8 alkane substrates via butane monooxygenase (BMO) were examined. Striking differences were observed in response to even- versus odd-chain-length alkanes. Propionate, the downstream product of propane oxidation and of the oxidation of other odd-chain-length alkanes followin...

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...

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...

We prove that the weak Morrey space WM is contained in $$M_{{q_1}}^p$$ for 1 ≤ q1 < q p ∞. As applications, we show if commutator [b, T] bounded from Lp to Lp,∞ some ∈ (1, ∞), then b BMO, where T a Calderón-Zygmund operator. Also, ∞, BMO and only [6, M . For belonging Lipschitz class, obtain similar results.

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...