A function f 2 L 1 (R) tiles the line with a constant weight w using the discrete tile set A if P a2A f(x ? a) = w almost everywhere. A set A is of bounded density if there is a constant C such that #fa 2 A : n a n + 1g C for all integers n. This paper characterizes compactly supported f 2 L 1 (R) that admit a tiling of R of bounded density. It shows that for such functions all tile sets of bou...

It is shown that maximal truncations of nonconvolution L-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1, 1) and L bounded for 1 < p < ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the bounded...

Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L 2-loss function. The unknown function f is assumed to be m times diierentiable except for an unknown, though nite, number of jumps, with piecewise mth derivative bounded in L 2-norm. An estimator is constructed, attaining the same o...

In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a conditional gauge theorem for these diffusions in bounded Lipschitz domains. Informally the Schrödinger-type operators we consider are of the form L + μ · ∇ + ν where ...

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

‎We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives‎ ‎of global normalizing factors associated to intertwining operators for the following reductive groups over number fields‎: ‎inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$‎. ‎This estimate is a key in...

The Kuratowski measure of noncompactness α on an infinite dimensional Banach space (X, ‖ · ‖) assigns to each bounded set S in X a nonnegative real α(S) by the formula α(S) = inf{δ > 0 | S = n ⋃ i=1 Si for some Si with diam(Si) ≤ δ, for 1 ≤ i ≤ n <∞}. In general a map β which assigns to each bounded set S in X a nonnegative real and which shares most of the properties of α is called a homogeneo...

Improving upon a recent result of L. Coburn and J. Xia, we show that for any bounded linear operator T on the Segal-Bargmann space, the Berezin transform of T is a function whose partial derivatives of all orders are bounded. Similarly, if T is a bounded operator on any one of the usual weighted Bergman spaces on a bounded symmetric domain, then the appropriately defined “invariant derivatives”...

Let L be a simply-connected simple connected algebraic group over number field F, and H semisimple absolutely maximal F-subgroup of L. $$\Delta (H)$$ the image diagonally embedded in $$L^n$$ . Under cohomological condition, we prove an asymptotic formula for rational points bounded height on projective equivariant compactifications (H)\backslash L^n$$ with respect to balanced line bundle.

Weighted norm inequalities for singular integral operators appear naturally in many areas of analysis, probability, operator theory ect. The one-weight case is now pretty well understood, and the answers are given by the famous Helson–Szegö theorem and the Hunt–Muckenhoupt–Wheden Theorem. The fist one state that the Hilbert Transform H is bounded in the weighted space L(w) if and only if w can ...