STEIN and TAIFJLESON gave a characterization for f E Lp(IRn) to be in the spaces L i p ( a , Lp) and Zyg(a, L p ) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (cp, L M ) and Zygmund-Orlicz spaces Zyg (cp, L M ) and to the general function cp E P instead of the power function cp(t) = t a . Such results describe the behavior of the Lapl...

We study regularity properties of solutions to operator equations on patchwise smooth manifolds ∂Ω such as, e.g., boundaries of polyhedral domains Ω ⊂ R3. Using suitable biorthogonal wavelet bases Ψ, we introduce a new class of Besov-type spaces Bα Ψ,q(Lp(∂Ω)) of functions u : ∂Ω → C. Special attention is paid on the rate of convergence for best n–term wavelet approximation to functions in thes...

Some simplifications of Schaffer's girth and perimeter of the unit spheres are introduced. Their general properties are discussed, and they are used to study the lp, Lp spaces, uniformly nonsquare spaces, and their isomorphic classes. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 46 B 20.

We consider multivariate integration in the weighted spaces of functions with mixed first derivatives bounded in Lp norms and the weighted coefficients introduced via `q norms, where p, q ∈ [1,∞]. The integration domain may be bounded or unbounded. The worst-case error and randomized error are investigated for quasi-Monte Carlo quadrature rules. For the worst-case setting the quadrature rule us...

The paper concerns finite-difference scheme for the approximation of partial differential equations in R1, with additional stochastic noise. By replacing the space derivatives in the original stochastic partial differential equation (SPDE, for short) with difference quotients, we obtain a system of stochastic ordinary differential equations. We study the difference between the solution of the o...

The paper concerns finite-difference scheme for the approximation of partial differential equations in R1, with additional stochastic noise. By replacing the space derivatives in the original stochastic partial differential equation (SPDE, for short) with difference quotients, we obtain a system of stochastic ordinary differential equations. We study the difference between the solution of the o...

We study an analogue of the classical theory of Ap(μ) weights in Rn without assuming that the underlying measure μ is doubling. Then, we obtain weighted norm inequalities for the (centered) Hardy-Littlewood maximal function and corresponding weighted estimates for nonclassical CalderónZygmund operators. We also consider commutators of those CalderónZygmund operators with bounded mean oscillatio...

Let Qm,n (with m≤ n) denote the space of polynomials of degree 2m or less on (−∞,∞), weighted by (1 + x2)−n. The elements Qm,n are thus rational functions with denominator (1 + x2)m and numerator of degree at most 2m (if m = n, we can write, more briefly, Qn for Qn,n). The spaces Qm,n form a nested sequence as n increases and r = n−m is held to some given value of weighted polynomial spaces, wi...