The weak type maximal principles of Stein and Sawyer are extended to nets operators defined on classes functions general measure spaces (possibly infinite measure), including the case locally compact groups. Applications differentiation

We discuss a method of producing computer assisted proofs of almost everywhere strong convergence of the d-dimensional Gauss algorithm. This algorithm is equivalent to Brun's algorithm and to the modi ed Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a nite number of calculations. These calculations have been carried out...

A risk neutral buyer observes a private signal s ∈ [a, b], which informs her that the mean and variance of a normally distributed risky asset are s and σ s respectively. She then sets a price at which to acquire the asset owned by risk averse “outsiders”. Assume σ s ∈ { 0, σ } for some σ > 0 and let B = { s ∈ [a, b] | σ s = 0 } . If B = ∅, then there exists a fully revealing equilibrium in whic...

It is of main interest in the theory of Fourier series the reconstruction of a function from the partial sums of its Fourier series. Just to mention two examples: Billard proved [2] the theorem of Carleson for the Walsh-Paley system, that is, for each function in L we have the almost everywhere convergence Snf → f and Fine proved [4] the Fejér-Lebesgue theorem, that is for each integrable funct...

CIPRIAN DEMETER, TERENCE TAO, AND CHRISTOPH THIELE Abstract. We establish multilinear L bounds for a class of maximal multilinear averages of functions on one variable, reproving and generalizing the bilinear maximal function bounds of Lacey [13]. As an application we obtain almost everywhere convergence results for these averages, and in some cases we also obtain almost everywhere convergence ...