It is well known that this limit exists a.e. for all f ∈ L, 1 ≤ p < ∞. In this paper, we will consider the oscillation and variation of this family of operators as goes to zero, which gives extra… (More)

In this paper we continue our investigations of square function inequalities in harmonic analysis. Here we investigate oscillation and variation inequalities for singular integral operators in… (More)

We have performed an ecliptic imaging survey of the Kuiper belt with our deepest and widest field achieving a limiting flux of m(g)50% ∼ 26.4, with a sky coverage of 3.0 square-degrees. This is the… (More)

In this paper we establish a variety or results in ergodic theory by using techniques from probability and analysis We discuss divergence of operators including strong sweeping out and Bourgain s… (More)

Let T be an ergodic transformation of a nonatomic probability space f an L function and K an integer It is shown that there is another L function g such that the joint distribution of T g i K is… (More)

Let x, e > 0, uo < ... u<? d' and h > O be real numbers. Let f be a real valued function and let A (h; u, w)f (x) h-d be a difference quotient associated with a generalized Riemann derivative. Set I… (More)

We show that in any invertible, ergodic, measure-preserving system, the two-sided square function obtained by comparing forward averages with their backwards counterparts, will diverge if the (time)… (More)

We present I and B photometry of five distinct transits of the exoplanet OGLE-TR-10b. By modeling the light curves, we find the planetary radius to be RP = 1.06 ± 0.08 RJup and the stellar radius to… (More)