Abstract We discuss a parabolic version of the space functions bounded mean oscillation related to doubly nonlinear partial differential equation. Parabolic John–Nirenberg inequalities, which give exponential decay estimates for function, are shown in natural geometry Chaining arguments applied change time lag inequality. also show that quasihyperbolic boundary condition is necessary and suffic...

Functions of bounded mean oscillation (BMO) play an important role in complex function theory and harmonic analysis. In this paper a sampling theorem for bandlimited BMO-functions is derived for sampling points that are the zero sequence of some sine-type function. The class of sinetype functions is large and, in particular, contains the sine function, which corresponds to the special case of e...

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We extend the classical Bernstein inequality to a general setting including Laplace-Beltrami operator, Schrödinger operators and divergence form elliptic on Riemannian manifolds or domains. prove $$L^p$$ inqualities as well “reverse inequality” which is new even for compact (with without boundary). Such reverse can be seen dual of inequality. The heat kernel will backbone our approach but we al...

The space CMO of functions of finite central mean oscillation is an analogue of BMO where the condition that the sharp maximal function is bounded is replaced by the convergence of the sharp function at the origin. In this paper it is shown that each element of CMO is a singular integral image of an element of the Beurling space B2 of functions whose Hardy-Littlewood maximal function converges ...

We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m, n), for m and n natural numbers. We use the ideas developed by Nazarov and Volberg in [NV] to prove that the weighted L(w)-norm of a paraproduct with complexity (m, n), associated to a function b ∈ BMO, depends linearly on the A2-characteristic of the weight w, linearly o...

Higher order entropies are kinetic entropy estimators suggested by Enskog expansion of Boltzmann entropy. These quantities are quadratic in the density ρ, velocity v and temperature T renormalized derivatives. We investigate asymptotic expansions of higher order entropies for compressible flows in terms of the Knudsen ǫk and Mach ǫm numbers in the natural situation where the volume viscosity, t...