Suppose a sequence of random variables fX n g has negative drift when above a certain threshold and has increments bounded in L p. When p > 2 this implies that EX n is bounded above by a constant independent of n and the particular sequence fX n g. When p 2 there are counterexamples showing this does not hold. In general, increments bounded in L p lead to a uniform L r bound on X + n for any r ...

Here φ(x) is a smooth cutoff function that localizes the surface S near some specific y ∈ S. The goal here is to determine the values of p for which M is bounded on L. The earliest work on this subject was done in the case where S is a sphere, when Stein [St1] showed M is bounded on L iff p > n+1 n for n > 1. This was later generalized by Greenleaf [Gr] to surfaces of nonvanishing Gaussian curv...

We show that L(R) absoluteness for semi-proper forcings is equiconsistent with the existence of a remarkable cardinal, and hence by [6] with L(R) absoluteness for proper forcings. By [7], L(R) absoluteness for stationary set preserving forcings gives an inner model with a strong cardinal. By [3], the Bounded Semi-Proper Forcing Axiom (BSPFA) is equiconsistent with the Bounded Proper Forcing Axi...

For a left vector space V over a totally ordered division ring F, let Co(V ) denote the lattice of convex subsets of V . We prove that every lattice L can be embedded into Co(V ) for some left F-vector space V . Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional, and L embeds into a finite lower bounded lattice of the form Co(V,Ω) = {X ∩Ω | X ∈ Co(V )}, for some f...

I fhI is the respective Haar coefficient, and σ(I) = ±1. This operator, which we denote by Tσ, is a dyadic martingale transform. The martingale transform is bounded as an operator on L(R,C). We want to find a condition on matrix weights, U and V , that implies that all martingale transforms are uniformly bounded as operators from L(R,C, V ) to L(R,C, U) where L(R,C, V ) is the space of function...

According to Chajda and Eigenthaler ([1]), a d-lattice is a bounded lattice L satisfying for all a, c ∈ L the implications (i) (a, 1) ∈ θ(0, c) → a ∨ c = 1; (ii) (a, 0) ∈ θ(1, c) → a ∧ c = 0; where θ(x, y) denotes the least congruence on L containing the pair (x, y). Every bounded distributive lattice is a d-lattice. The 5-element nonmodular lattice N 5 is a d-lattice. Theorem 1 A bounded latti...

This paper first proves the Savitch Theorem: any nondeterminstic L(n)− tape bounded Turing Machine can be simulated by a deterministic [L(n)]− tape bounded Turing machine, provided L(n) ≥ log2n. Then as an attempt to answer the following question: “Given a nondeterministic tape bounded Turing machine which accepts set A, how much additional storage does a deterministic Turing machine require to...

In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L-cohomology of these manifolds: if e.g. a manifold admits a metric of bounded geometry which outside a compact set has nonnegative Ricci curvature and nonnegative mean curvature (of the bo...

Let G denote a locally compact Hausdorff abelian group. Then a bounded linear operator T from L^2(G) into L^2(G) is a bounded multiplier operator if, under the Fourier transform on L^2(G ), for each function f in L^2(G), T(f) changes into a bounded function U times the Fourier transform of f. Then U is called the multiplier of T. An unbounded multiplier operator has a similar definition, but it...

Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and (q−(L), q+(L)) be the maximal interval of exponents q ∈ [1, ∞] such that the gradient semigroup { √ t∇e}t>0 is bounded on L(R). In this article, the authors establish the non-tangential maximal function characterizations of the associated Hardy spaces H L(R) for all p ∈ (0, q+(...