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Weighted multidimensional inequalities for monotone functions

Sorina BarzaLars-Erik Persson — 1999

Mathematica Bohemica

We discuss the characterization of the inequality (RN+ fq u)1/q C (RN+ fp v )1/p,   0<q, p <, for monotone functions f 0 and nonnegative weights u and v and N 1 . We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions.

Distribution and rearrangement estimates of the maximal function and interpolation

Irina AsekritovaNatan KrugljakLech MaligrandaLars-Erik Persson — 1997

Studia Mathematica

There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous...

Clarkson type inequalities and their relations to the concepts of type and cotype.

Mikio KatoLars-Erik. PerssonYasuji Takahashi — 2000

Collectanea Mathematica

We prove some multi-dimensional Clarkson type inequalities for Banach spaces. The exact relations between such inequalities and the concepts of type and cotype are shown, which gives a conclusion in an extended setting to M. Milman's observation on Clarkson's inequalities and type. A similar investigation conceming the close connection between random Clarkson inequality and the corresponding concepts of type and cotype is also included. The obtained results complement, unify and generalize several...

Structure of the Hardy operator related to Laguerre polynomials and the Euler differential equation.

Natan KruglyakLech MaligrandaLars-Erik Persson — 2006

Revista Matemática Complutense

We present a direct proof of a known result that the Hardy operator Hf(x) = 1/x ∫ f(t) dt in the space L = L(0, ∞) can be written as H = I - U, where U is a shift operator (Ue = e, n ∈ Z) for some orthonormal basis {e}. The basis {e} is constructed by using classical Laguerre polynomials. We also explain connections with the Euler differential equation of the first order y' - 1/x y = g and point out some generalizations to the case with weighted L (a, b) spaces.

A study of bending waves in infinite and anisotropic plates

Ove LindblomReinhold NäslundLars-Erik PerssonKarl-Evert Fällström — 1997

Applications of Mathematics

In this paper we present a unified approach to obtain integral representation formulas for describing the propagation of bending waves in infinite plates. The general anisotropic case is included and both new and well-known formulas are obtained in special cases (e.g. the classical Boussinesq formula). The formulas we have derived have been compared with experimental data and the coincidence is very good in all cases.

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