We consider the generalized Lorentz space L_ψ,q defined via a continuous and concave function ψ and the Fourier series of a function with respect to an unbounded orthonormal system. Some new Fourier and Jackson-Nikol’skii type inequalities in this frame are stated, proved and discussed. In particular, the derived results generalize and unify several well-known results but also some new applications ...

We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n∈Nn∈N. Some new Hardy-type inequalities for this operator are proved and discussed.

A multidimensional Cochran-Lee operator is introduced and investigated in the frame of Hardy-type inequalities with parameters 0<p⩽q<∞. Moreover, for the case p=q and power weights even the sharp constant is derived, thus generalizing the original Cochran-Lee inequality to a multidimensional setting. As applications both several known but also new inequalities are pointed out.

We prove and discuss some new refined Hölder inequalities for any p>1 and also a reversed version for 0<p<1. The key is to use the concepts of superquadraticity, strong convexity, and to first prove the corresponding refinements of the Young and reversed Young inequalities. Refinements of the Minkowski and reversed Minkowski inequalities are also given.

The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a two-sided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253).

We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some "optimal" weights these new operators are bounded from the martingale Hardy space H_p(G) to the space weak-L_p(G), for 0 <p<1/2. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.

We prove and discuss some new weak type (1, 1) inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are pointed out.

Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle, we introduce the notions of steady state and weak steady state. We establish the continuity of weak steady states for an ergodic and uniformly elliptic environment. ...

Marine noise reduction tends to be challenging and requires a comprehensive engineering approach. The soundproofing materials for marine noise reduction are usually exposed to high temperatures, potential fluid or oil spills, engine maintenance and a high airflow environment. This work looks into the acoustic proofing properties of a non-toxic material ‘SK One Component Polyurethane’ developed by ...