On some pointwise inequalities

In a recent paper (Studia Math. 138 (2000) 285-291) we proved pointwise estimates relating some classical maximal and singular integral operators. Here we show that, in a sense, there are more flexible inequalities which not only imply the previously known results but also give something new. In particular, they hold for the multilinear Calderón-Zygmund operators. This result gives a new approach to a recent work by Grafakos and Torres, and unifies some classical inequalities by Cotlar and Coifman and Fefferman.     

On some composite functional inequalities

The aim of the paper is to deal with the following composite functional inequalities

On some inequalities for polynomials

We prove the equivalence between analogs of the Paley and Nikol’skii inequalities for any orthonormal system of functions and for almost periodic polynomials with arbitrary spectrum. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1289–1292, September, 1998.     

On some new Hilbert-type inequalities

In the present paper we establish some new inequalities similar to extensions of Hilbert’s double-series inequality and give also their integral analogues. Our results provide some new estimates to these types of inequalities.     

On some new discrete inequalities

Some new discrete inequalities involving higher order differences have been obtained here. These inequalities can be used in the analysis of a class of summary difference equations as handy tools. Some applications are also given.     

On some degenerate evolution variational inequalities

Summary A class of parabolic variational inequalities is investigated, where: the unilateral constraints concern the time derivative of the unknown function; degeneracies or singularities with respect to the time variable are considered. Some general abstract existence and uniqueness results are proved, in the natural framework of suitable weighted spaces.

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Sunto Si studia una classe di disequazioni variazionali paraboliche, dove: i vincoli unilaterali riguardano la derivata rispetto al tempo delta funzione incognita; vengono considerate singolarità e degenerazioni rispetto alla variabile temporale. Si dimostrano alcuni risultati generali di esistenza ed unicità, nell'ambito naturale di opportuni spazi con peso.

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This work was supported in part by the «G.N.A.F.A. del C.N.R.», and by the «Ministero dell'Università e della Ricerca Scientifica» (through 60% and 40% grants).     

On some inequalities of local time

In this paper, we extend the Barlow-Yor's inequality of local time to the case stopped at a random time.     

On some fundamental partial integral inequalities

This paper presents several new partial integral inequalities in two independent variables which can be used in the analysis of various problems in the theory of partial differential and integral equations as ready and powerful tools. An elementary technique of reducing the integral inequality to second order partial differential inequality and then integrating it by Riemann's method is used to establish our results.     

On some sharp weighted norm inequalities

Given a weight ω, we consider the space which coincides with when ω∈A_p. Sharp weighted norm inequalities on for the Calderón-Zygmund and Littlewood-Paley operators are obtained in terms of the A_p characteristic of ω for any 1<p<∞.