Related papers: Sur les estimations du type sup+inf et sup*inf

New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

This paper gives a priori estimates for the positve solutions of Kirchhoff type equation without variational structure.

We give an inequality of type sup+Cinf in dimension 2.

Explicit formulae for Weber-Schafheitlin's type integrals with exponent 1 are derived. The results of these integrals are distributions on R_+.

We introduce notions of bi-unitary, bi*-unitary and bi**-unitary harmonic numbers, along with their preliminary study.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

Estimates of some integrals related to variations of smooth functions are presented.

We study the fourth order Schr\"odinger type differential inequality $-\Delta^2 u + \lambda V(x)u \geq a(x)u^q$ with $a,V\in L^1_{loc}(\mathbf{R}^N)$, both nonnegative, and $\lambda>0$. We consider nonnegative solutions without making any…

In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…

We establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the independent variables.

We present some old and new results on dispersive estimates for Schroedinger equations.

We establish several sum-product estimates over finite fields that involve polynomials and rational functions. First, |f(A)+f(A)|+|AA| is substantially larger than |A| for an arbitrary polynomial f over F_p. Second, a characterization is…

We estimate the number of integer solutions to decomposable form inequalities (both asymptotic estimates and upper bounds are provided) when the degree of the form and the number of variables are relatively prime. These estimates display…

We discuss some estimates of subelliptic type related with vector fields satisfying the H\"ormander condition. Our approach makes use of a class of approximate exponentials maps. Such kind of estimates arises naturally in the study of…

In this short note, we obtain error estimates for Riemann sums of some singular functions.

We give an abstract argument that an a priori Fourier restriction estimate for a certain choice of exponents automatically implies maximal and variational Fourier restriction estimates. These, in turn, provide pointwise and quantitative…

I give some claims on primorial prime numbers for interested readers in number theory.

In this paper we present some new upper bounds of the Cusa-Huygens and the Huygens approximations. Bounds are obtained in the forms of some polynomial and some rational functions.

We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…