Related papers: A remark on an endpoint Kato-Ponce inequality
In this paper we discuss cylindrical extensions of improved Hardy, Sobolev type and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants and identities in the spirit of Badiale-Tarantello [2]. All identities are obtained in the…
The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved,…
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
In this paper we prove the Fractional Gagliardo-Nirenberg Inequality, Polya-Szego Inequality and the Sharp Fractional Sobolev Inequality, we then provide an application of such inequalities in a constraiend variational problem involving the…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples.…
We prove a family of improved multipolar Poincar\'e-Hardy inequalities on Cartan-Hadamard manifolds. For suitable configurations of poles, these inequalities yield an improved multipolar Hardy inequality and an improved multipolar…
We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj\"orner--Wachs inequality and generalize it to inequalities on order polynomials and their $q$-analogues via direct…
In the monograph Kounchev, O. I., Multivariate Polysplines. Applications to Numerical and Wavelet Analysis, Academic Press, San Diego-London, 2001, and in the paper Kounchev O., Render, H., Cardinal interpolation with polysplines on annuli,…
In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…
We present a simple proof of some interpolation inequalities between H\"{o}lder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate…
In this paper, we give a characterization of the two weight strong and weak type norm inequalities for the bilinear fractional integrals. Namely, we give the characterization of the following inequalities, \[ \|\mathcal I_\alpha…
A new approach to classical self improving results for $BMO$ functions is presented. "Coordinate Gagliardo spaces" are introduced and a generalized version of the John-Nirenberg Lemma is proved. Applications are provided.
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…
This note proves a version of Lubell-Yamamoto-Meshalkin inequality for general product measures.
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
We show that a recent interpolative new proof of the Bohnenblust--Hille inequality, when suitably handled, recovers its best known constants. This seems to be unexpectedly surprising since the known interpolative approaches only provide…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
We give an explicit formula for one possible Bellman function associated with the $L^p$ boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same Bellman function in various other settings,…