Related papers: Two local inequalities
We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for $k$-cones. These are extensions of results \L aba and Pramanik to sharp exponents.
We establish upper bounds for the convolution operator acting between interpolation spaces. This will provide several examples of Young Inequalities in different families of function spaces. We use this result to prove a bilinear…
n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…
In this paper, we establish a general inequality for locally strongly convex centroaffine hypersurfaces in $\mathbb{R}^{n+1}$ involving the norm of the covariant derivatives of both the difference tensor $K$ and the Tchebychev vector field…
The paper proposes and motivates a conjecture on the invariance of cohomological support loci under derived equivalence. It contains a proof in the case of surfaces, and explains further developments and consequences.
Some companions of Gruss inequality in inner product spaces and applications for integrals are given.
Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local…
We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.
We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.
Local divisors allow a powerful induction scheme on the size of a monoid. We survey this technique by giving several examples of this proof method. These applications include linear temporal logic, rational expressions with Kleene stars…
In this paper we study the local behavior of a solution to the Lam\'e system when the Lam\'e coefficients $\lambda$ and $\mu$ satisfy that $\mu$ is Lipschitz and $\lambda$ is essentially bounded in dimension $n\ge 2$. One of the main…
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which…
In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.
In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant entropy inequalities. We obtain new inequalities on functional…
We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in $\mathbb{R}^5$ given by two quadratic forms in three variables. Together with previous work by Demeter, Guo, and Shi in the non-degenerate case…
We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for…
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
Local boundedness and Harnack inequalities are studied for solutions to parabolic and elliptic integro-differential equations whose governing nonlocal operators are associated with nonsymmetric forms. We present two independent proofs, one…
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical…
We use a dual mesh numerical method to study a non-local parabolic problem arising from the well-known thermistor problem.