Related papers: The Marcinkiewicz multiplier theorem revisited
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We proved three theorems of $S$-version of the mulyiplicity one.
We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric…
We present a proof of completeness for the implicational propositional calculus, based on a variant of the Lindenbaum procedure.
Let $\Omega$ be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and $\mathcal{M}_{\Omega}$ be the higher-dimensional Marcinkiewicz integral associated with $\Omega$. In this paper, the author considers…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
The aim of this work is the study of the Weinstein $L^2$- multiplier operators on $\mathbb{R}^{d+1}_+$ and we give for them Calder\'on's reproducing formulas and best approximation using the theory of Weinstein transform and reproducing…
We establish several variants of the multilinear multiplier theorem of Coifman and Meyer. We also present examples that are not covered by existing theories. Our motivation comes from applications to the definition of the Jacobian and…
Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.
We construct a De Morgan algebra-valued logic with quantifiers, where the truth values are in a finite De Morgan algebra, We show that there is a representation theorem of the cylindric algebra of this logic from which a completeness…
The sub-linear expectation space is a nonlinear expectation space having advantages of modelling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace…
In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.
The aim of this paper is to characterize and construct universally optimal designs among the class of circular repeated-measurements designs when the parameters do not permit balance for carry-over effects. It is shown that some circular…
Our first result is a statement of a somewhat general form of a non-substitution theorem for linear programming problems, along with a very easy proof of the same. Subsequently, we provide an easy proof of theorem 1 in a 1979 paper of Olvi…
We present a new and simple proof of a theorem due to Kaplansky which unifies theorems of Kolchin and Levitzki on triangularizability of semigroups of matrices. We also give two different extensions of the theorem. As a consequence, we…
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…
We give new a proof of the general Brian\c{c}on-Skoda theorem about ideals of holomorphic functions by means of multivariable residue calculus. The method gives new variants of this theorem for products of ideals. Moreover, we obtain a…
Given Mikhlin-H\"ormander multipliers $m_i$, $i=1,..., N$, with uniform estimates we prove an optimal $\sqrt{\log(N+1)}$ bound in $L^p$ for the maximal function $\sup_i|\cF^{-1}[m_i\hat f]|$ and related bounds for maximal functions…
Based on various strategies and a new general doubling operator, we obtain several simple proofs of the celebrated Sharkovsky's cycle coexistence theorem. A simple non-directed graph proof which is especially suitable for a calculus course…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…