Related papers: Burkholder inequality by Bregman divergence
In this paper we prove an inequality for individual and uniform Diophantine exponents in the case of simultaneous approximation. This inequality is better than Jarnik's for small values of the uniform exponent.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We prove a result on the existence of linear forms of a given Diophantine type.
In this paper we give necessary and sufficient conditions for the equality case in Wielandt's eigenvalue inequality.
We prove the self-improvement of a pointwise $p$-Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.
We make the final step to give a proof for the Brannan's conjecture. The basic tool of the study is a Mac-Laurin development and an adequately estimation of an integral.
A generalization of the law of total covariance is presented and proved.
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
We prove several congruences for trinomial coefficients.
A proof of Sendov's conjecture is given.
We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings.
An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
In this paper, we prove a Pr\'ekopa-Leindler type inequality of the $L_p$ Brunn-Minkowski inequality. It extends an inequality proved by Das Gupta [8] and Klartag [16], and thus recovers the Pr\'ekopa-Leindler inequality. In addition, we…
We prove a version of adelic descent for continuous localizing invariants.
We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.
We prove an analogue of the Lagrange Inversion Theorem for Dirichlet series. The proof is based on studying properties of Dirichlet convolution polynomials, which are analogues of convolution polynomials introduced by Knuth in [4].
We prove a uniformization theorem in complex algebraic geometry.
We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.