Maximal functions and capacities
نویسندگان
چکیده
منابع مشابه
LC-functions and maximal monotonicity
In this paper, we consider LC–functions, a class of special convex functions from the product of a reflexive Banach space and its dual into ]−∞,∞]. Using Fitzpatrick functions, we will show that the theory of LC–functions is a proper extension of the theory of maximal monotone sets. Various versons of the Fenchel duality theorem lead to a number of results on maximal monotonicity, some of them ...
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Abstract. We consider the integrability of φ(f∗) for various maximal functions f∗ and various increasing functions φ. We show that for some of the standard maximal functions arising in harmonic analysis and ergodic theory, there is never integrability of φ(f∗) for all Lebesgue integrable functions f except in cases where the growth of φ is slow enough so that the integrability follows from the ...
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The bilinear maximal operator defined below maps L × L into L provided 1 < p, q <∞, 1/p+ 1/q = 1/r and 2/3 < r ≤ 1. Mfg(x) = sup t>0 1 2t ∫ t −t |f(x+ y)g(x− y)| dy In particular Mfg is integrable if f and, g are square integrable, answering a conjecture posed by Alberto Calderón. 1 Principal Results In 1964 Alberto Calderón defined a family of maximal operators by Mfg(x) = sup t>0 1 2t ∫ t −t ...
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Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Mor...
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We prove the existence of a limitwise monotonic function g : N→ N \ {0} such that, for any Π1 function f : N → N \ {0}, Ran f 6= Ran g. Relativising this result we deduce the existence of an η-like computable linear ordering A such that, for any Π2 function F : Q → N \ {0}, and η-like B of order type ∑ {F (q) | q ∈ Q }, B A . We prove directly that, for any computable A which is either (i) stro...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1965
ISSN: 0373-0956
DOI: 10.5802/aif.195