The BMO norm of / is equivalent to sup (f\f(y)-u(x,t)\"Pt(x-y)dy\ , where Pt is the Poisson kernel. In this note, we show that Pt can be replaced by a nonnegative radial function h, which is positive in a neighbourhood of 0, with J h(x) dx = 1 and J rTM" (Inr)h(r) dr < oo, where h is the least decreasing radial majorant of h. 1980 Mathematics subject classification (Amer. Math. Soc): primary 42...

fails to possess a solution in general if X is equal to any of the characteristic values X¡, ¿ = 1,2,3, , of the kernel __(x, y), it is not surprising that all treatments of (1) have been limited to the cases in which equation (2) is in some sense (to be made more precise later) a majorant for (1) when X =Xi, the smallest characteristic value of F"(x, y). Thus, if FT(x, y) is assumed to be posi...

fails to possess a solution in general if X is equal to any of the characteristic values X¡, ¿ = 1,2,3, , of the kernel __(x, y), it is not surprising that all treatments of (1) have been limited to the cases in which equation (2) is in some sense (to be made more precise later) a majorant for (1) when X =Xi, the smallest characteristic value of F"(x, y). Thus, if FT(x, y) is assumed to be posi...

In this paper the problem of practical stabilization for a significant class of MIMO uncertain pseudo-linear and pseudoquadratic systems, with additional bounded nonlinearities and/or bounded disturbances, is considered. By using the concept of majorant system, via Lyapunov approach, new fundamental theorems, from which derive explicit formulas to design state feedback control laws, with a poss...

We extend the isotonic analysis for Wicksell's problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in astronomy. The main result is a version of the Kiefer–Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate n −1 log n faster than n −2/3 log n. The main result is useful ...

this paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎with the help of the nehari manifold and palais-smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a certai...

We propose a penalized method for the least squares estimator of a multivariate concave regression function. This estimator is formulated as a quadratic programming (QP) problem with O(n) constraints, where n is the number of observations. Computing such an estimator is a very timeconsuming task, and the computational burden rises dramatically as the number of observations increases. By introdu...

Let f(z) akzk a 0 be analytlc in the unlt disc. Any k=O o Inflnlte complex vector e (eo,et,e2 ) such that lekl 1, k 0,1,2 induces a function re(Z) akekZk whlch is still analytic k=O In the unit disc. In this paper we study the problem of maximizing the p-means: over all possible vectors e and for values of r close to 0 and for all p<2. k It is proved that a maxlmlzlng function Is f,{z} -laoi + ...

Abstract In this work we study d-dimensional majorant properties. We prove that a set of frequencies in $\mathbb{Z}^d$ satisfies the strict property on $L^p([0,1]^d)$ for all p &amp;gt; 0 if and only is affinely independent. further construct three types violations property. Any at least d + 2 violates an open interval $p \not\in 2\mathbb{N}$ length 2. infinite sequence intervals Finally, given...