Related papers: The Marcinkiewicz multiplier theorem revisited

This article is concerned with the question of whether Marcinkiewicz multipliers on $\mathbb R^{2n}$ give rise to bilinear multipliers on $\mathbb R^n\times \mathbb R^n$. We show that this is not always the case. Moreover we find necessary…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms…

We extend an $L^2$ maximal multiplier result of Bourgain to all $L^p$ spaces, $1<p<\infty$.

We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods).

Sufficient ultraspherical multiplier criteria are refined in such a way that they are comparable with necessary multiplier conditions. Also new necessary conditions for Jacobi multipliers are deduced which, in particular, imply known Cohen…

We prove pointwise relations between some multiparameter square functions on $\bold R^n$.

We provide algorithms for the absolute and alternating Ostrowski Expansions of the continuum and provide proofs for their uniqueness.

In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.

We prove some new results related to Tanaka's formula.

We present a new, elementary, dynamical proof of the prime number theorem.

We prove a Marcinkiewicz testing condition for the boundedness of Schur multipliers on the Schatten $p$-classes. This generalizes a previous work of J. Bourgain for Toeplitz type Schur multipliers. As a corollary, we obtain a new…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.

In this paper we study sharp generalizations of $\dot{F}_p^{0,q}$ multiplier theorem of Mikhlin-H\"ormander type. The class of multipliers that we consider involves Herz spaces $K_u^{s,t}$. Plancherel's theorem proves…

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the…

We prove an infinitary version of the Brauer-Schur theorem.

We define a version of multiplier ideals, the Mather multiplier ideals, on a variety with arbitrary singularities, using the Mather discrepancy and the Jacobian ideal. In this context we prove a relative vanishing theorem, thus obtaining…

We prove the existence of maximizers for a general family of restrictions operators, up to the end-point. We also provide some counterxamples in the end-point case.

This paper establishes complete convergence for weighted sums and the Marcinkiewicz--Zygmund-type strong law of large numbers for sequences of negatively associated and identically distributed random variables $\{X,X_n,n\ge1\}$ with general…