Pólya-type polynomial inequalities in Orlicz spaces and best local approximation

Best Simultaneous Approximation in Orlicz Spaces

Best Constants in Kahane-Khintchine Inequalities in Orlicz Spaces

Several inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. For this the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the well-known estimates for subnormal random variables, see [9], the third one is a consequence of a certain Gaussian-Jensen’s majorization technique, see [6], and the f...

Research Article Best Simultaneous Approximation in Orlicz Spaces

Recommended by Ricardo Estrada Let X be a Banach space and let L Φ (I,X) denote the space of Orlicz X-valued integrable functions on the unit interval I equipped with the Luxemburg norm. In this paper, we present a distance formula dist Φ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in a...

Whitney type inequalities for local anisotropic polynomial approximation

We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in Lp(Q) with 1 ≤ p ≤ ∞. Here Q is a d-parallelepiped in R with sides parallel to the coordinate axes. We consider the error of best approximation of a function f by algebraic polynomials of fixed degree at most ri− 1 in variable xi, i = 1, ..., d, and relate it to a so-called total mixed modulus of ...

Korn Inequalities In Orlicz Spaces

We use gradient estimates for solutions of elliptic equations to obtain Korn’s inequality for fields with zero trace from Orlicz–Sobolev classes. As outlined for example in the monographs of Málek, Nečas, Rokyta, Růžička [MNRR], of Duvaut and Lions [DL] and of Zeidler [Ze], the well-posedness of many variational problems arising in fluid mechanics or in the mechanics of solids heavily depends o...