منابع مشابه
The Intrinsic Square Function
We show that the Lusin area function and essentially all of its realvariable generalizations are pointwise dominated by an “intrinsic” square function, and that this latter function is, for all practical purposes, no larger than a “generic” square function. 0. Introduction. The Lusin area (or “square”) function is a familiar object. If f : R 7→ R is such that u(x, y) ≡ Py ∗ f(x), the Poisson in...
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We extend work of the author to show that the “intrinsic” square function, which pointwise dominates (and, in almost all ways, is easier to work with than) the familiar Lusin area function and its real-variable analogues, also defines a bounded operator on L(R, w dx) for all weights w in the Muckenhoupt Ap class (1 < p < ∞). We apply this result to get a strong weighted Littlewood-Paley inequal...
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The thermal mean-square displacement (MSD) of hydrogen in proteins and its associated hydration water is measured by neutron scattering experiments and used an indicator of protein function. The observed MSD as currently determined depends on the energy resolution width of the neutron scattering instrument employed. We propose a method for obtaining the intrinsic MSD of H in the proteins, one t...
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Previous findings have shown the many functions of nostalgia, for example, increasing mental health, and the current research aimed to explain those findings by testing the theoretical explanation that the benefits of nostalgia come from the fact that nostalgia reminds us of our intrinsic self. Aiming to investigate the effect of nostalgia on authenticity (intrinsic self-expression) and extrins...
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Given a ∈ Z \ {±1, 0}, we consider the problem of enumerating the integers m coprime to a such that the order of a modulo m is square free. This question is raised in analogy to a result recently proved jointly with F. Saidak and I. Shparlinski where square free values of the Carmichael function are studied. The technique is the one of Hooley that uses the Chebotarev Density Theorem to enumerat...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2007
ISSN: 0213-2230
DOI: 10.4171/rmi/512