The study of the nanometer-scale vacancy defects (nanopores) in graphene by transmission electron microscopy (TEM) is severely hindered presence polymeric residues originating from graphene-transfer-step to TEM grid. state-of-the-art transfer strategies yield contamination-free pristine specimens but do not work well for nanoporous graphene. This because relatively high energy vacant nanopores ...

J. L. Klay, N. N. Ajitanand, J. M. Alexander, M. G. Anderson, D. Best, F. P. Brady, T. Case, W. Caskey, D. Cebra, J. L. Chance, P. Chung, B. Cole, K. Crowe, A. C. Das, J. E. Draper, M. L. Gilkes, S. Gushue, M. Heffner, A. S. Hirsch, E. L. Hjort, L. Huo, M. Justice, M. Kaplan, D. Keane, J. C. Kintner, D. Krofcheck, R. A. Lacey, J. Lauret, C. Law, M. A. Lisa, H. Liu, Y. M. Liu, R. McGrath, Z. Mil...

where the implied constant is independent of n ≥ 1. The inequality above (without restriction on the coefficients) arises in connection to several areas, such as Probabilities, Approximation, and Discrepancy. With η(d) = (d − 1)/2, the inequality above follows from orthogonality, while it is conjectured that the inequality holds with η(d) = d/2. This is known and proved in (Talagrand, 1994) in ...

The study of directional maximal operators goes back at least to the works of Córdoba [Co1] and Strömberg [Str1] in the 70’s and is as recent as the results of Alfonseca, Soria and Vargas [ASV1], [ASV2], Karagulyan and Lacey [KL] and Bateman and Katz [Ba1], [BK1]. Progress in the area involved the work of many authors and we refer to [W], [ASV2], [KL] and references therein for historical backg...

We prove mixed Ap-Ar inequalities for several basic singular integrals, Littlewood–Paley operators, and the vector-valued maximal function. Our key point is that r can be taken arbitrarily big. Hence, such inequalities are close in spirit to those obtained recently in the works by T. Hytönen and C. Pérez, and M. Lacey. On one hand, the “Ap-A∞” constant in these works involves two independent su...