Weak type estimates associated to Burkholder's martingale inequality.
Weak Type Inequality for the Square Function of a Nonnegative Submartingale
Let f be a nonnegative submartingale and S(f) denote its square function. We show that for any λ > 0, , and the constant π/2 is the best possible. The inequality is strict provided ∥f∥₁ ≠ 0.
Weakly periodic sequences of bounded linear transformations: A spectral characterization.
Weakly stationary processes with non–positive autocorrelations
We deal with real weakly stationary processes with non-positive autocorrelations , i. e. it is assumed that for all . We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies for all are provided as well.
Weighted norm inequalities for martingales
Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces
Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis . Given an operator T from to L¹(X), we consider the vector-valued extension T̃ of T given by . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...
Weighted power variations of iterated Brownian motion.
What was Nicolo Tartaglia doing in the night to Ash Wednesday of the year 1523 in Verona. (Was machte Nicolo Tartaglia in der Nacht zum Aschermittwoch des Jahres 1523 in Verona.)
Which moments of a logarithmic derivative imply quasiinvariance.
Williams' characterisation of the brownian excursion law : proof and applications
Windings of planar random walks and averaged Dehn function
We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.
Within and beyond the reach of Brownian innovation.