The aim of this paper is to study semigroups possessing E-regular elements, where an element a of a semigroup S is E-regular if a has an inverse a◦ such that aa◦, a◦a lie in E ⊆ E(S). Where S possesses ‘enough’ (in a precisely defined way) E-regular elements, analogues of Green’s lemmas and even of Green’s theorem hold, where Green’s relations R,L,H and D are replaced by R̃E , L̃E , H̃E and D̃E . N...

INTRODUCTION Maximal strength is often estimated using the force-endurance relationship, where tables or formula are used to predict one repetition maximum (1RM) or other loads (e.g. 3RM loads). For some populations (for example the frail or very young) such a procedure may not be appropriate and the accuracy of these methods depends on several parameters such as the number of repetitions, type...

Surgeon, 1th Regiment M. N. I. 1 Hiatorical.?Sambalpur first comes before us in the epic which describes the famous exploits of Kama in his expedition against the demon Havana, and according to the legend, the warlike Rama largely recruited his monkey army from this locality. But let us leave the fabulous part of the story and give a brief account of the former history of Sambalpur. The first R...

where U is the class of all h∈ L2(R+,r−1dr) with ‖h‖L2(R+,r−1dr) ≤ 1. The operator Ω was introduced by Chen and Lin [7]. They showed that Ω is bounded on Lp(Rn) for all p > 2n/(2n− 1) provided that Ω ∈ (Sn−1). Recently, we have been able to show that the Lp(Rn) boundedness of Ω still holds for all p ≥ 2 if the condition Ω ∈ (Sn−1) is replaced by the more natural and weaker condition Ω ∈ L(logL)...

The relation between approach regions and singularities of nonnegative kernels Kt(x, y) is studied, where t ∈ (0,∞), x, y ∈ X, and X is a homogeneous space. For 1 ≤ p < q < ∞, a sufficient condition on approach regions Ωa (a ∈ X) is given so that the maximal function sup (x,t)∈Ωa ∫ X Kt(x, y)f(y) dσ(y) is weak-type (p, q) with respect to a pair of measures σ and ω. It is shown that this conditi...

A new proof of a weighted norm inequality for multilinear singular integrals of Calderón-Zygmund type is presented through a more general estimate involving a sharp maximal function. An application is given to the study of certain multilinear commutators.

In this paper some results on the structure of finite-dimensional Lie algebras are obtained by means of the concept of maximal abelian dimension. More concretely, a sufficient condition is given for the solvability in finite-dimensional Lie algebras by using maximal abelian dimensions. Besides, a necessary condition for the nilpotency is also stated for such Lie algebras. Finally, the maximal a...

For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a m...

We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W (R) × W (R) → W (R) with 1 < p, q < ∞ and r ≥ 1, boundedly and continuously. The same result holds on R when r > 1. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versi...

Let H ∼= R ⋉ R be the Heisenberg group and let μt be the normalized surface measure for the sphere of radius t in R. Consider the maximal function defined by Mf = supt>0 |f ∗ μt|. We prove for n ≥ 2 that M defines an operator bounded on L(H) provided that p > 2n/(2n− 1). This improves an earlier result by Nevo and Thangavelu, and the range for L boundedness is optimal. We also extend the result...