Sharp weak type (1, 1) and L p estimates in dimension one are obtained for uncentered maximal functions associated with Borel measures which do not necessarily satisfy a doubling condition. In higher dimensions uncentered maximal functions fail to satisfy such estimates. Analogous results for centered maximal functions are given in all dimensions.

One can view a 2-parameter Brownian sheet {W (s, t); s, t ≥ 0} as a stream of interacting Brownian motions {W (s, •); s ≥ 0}. Given this viewpoint, we aim to continue the analysis of Walsh (1978) on the local times of the stream W (s, •), near time s = 0. Our main result is a kind of maximal inequality that, in particular, verifies the following conjecture of Khoshnevisan (1995a): as s → 0, the...

Abstract: One can view a 2-parameter Brownian sheet {W (s, t); s, t ≥ 0} as a stream of interacting Brownian motions {W (s, •); s ≥ 0}. Given this viewpoint, we aim to continue the analysis of [20] on the local times of the stream W (s, •) near time s = 0. Our main result is a kind of maximal inequality that, in particular, verifies the following conjecture of [10]: As s → 0, the local times of...

the length of equal minimal and maximal blocks has eected on logarithm-scale logarithm against sequential function on variance and bias of de-trended uctuation analysis, by using quasi monte carlo(qmc) simulation and cholesky decompositions, minimal block couple and maximal are founded which are minimum the summation of mean error square in horest power.

We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are sharp.

We prove sharp estimates for Fourier transforms of indicator functions bounded open sets in $${\mathbb {R}}^n$$ with real analytic boundary, as well nontrivial lattice point discrepancy results. Both are derived from on hypersurface measures. Relations maximal averages discussed, connecting two conjectures Iosevich and Sawyer (Adv Math 132(1):46–119, 1997). also a theorem concerning the stabili...