Existence and non-existence of maximal solutions for y" = f(x, y, y') *
J. W. Bebernes, Steven K. Ingram (1971)
Annales Polonici Mathematici
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J. W. Bebernes, Steven K. Ingram (1971)
Annales Polonici Mathematici
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Frank Terpe (1971)
Colloquium Mathematicae
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M. A. Selby (1974)
Colloquium Mathematicae
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A. M. Stokolos (2006)
Colloquium Mathematicae
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The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.
Doroslovački, Rade, Pantović, Jovanka, Vojvodić, Gradimir (1999)
Novi Sad Journal of Mathematics
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Antonio Vera López, Gustavo A. Fernández Alcober (1989)
Extracta Mathematicae
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Detlef Müller (1990)
Colloquium Mathematicae
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Richard L. Wheeden (1993)
Publicacions Matemàtiques
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Sufficient conditions are derived in order that there exist strong-type weighted norm inequalities for some off-centered maximal functions. The maximal functions are of Hardy-Littlewood and fractional types taken over starlike sets in R. The sufficient conditions are close to necessary and extend some previously known weak-type results.
Kabe Moen (2009)
Studia Mathematica
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We investigate the boundedness of the fractional maximal operator with respect to a general basis on weighted Lebesgue spaces. We characterize the boundedness of these operators for one-weight and two-weight inequalities extending the work of Jawerth. A new two-weight testing condition for the fractional maximal operator on a general basis is introduced extending the work of Sawyer for the basis of cubes. We also find the sharp dependence in the two-weight case between the operator norm...
Haddad, Lucien, Lau, Dietlinde (2000)
Beiträge zur Algebra und Geometrie
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Eric Sawyer (1982)
Studia Mathematica
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Antonio Vera López, Gustavo A. Fernández Alcober (1989)
Extracta Mathematicae
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Alberto Criado, Fernando Soria (2016)
Studia Mathematica
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In recent work by Reguera and Thiele (2012) and by Reguera and Scurry (2013), two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal function were refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the value of the Hilbert transform is substantially bigger than that of the maximal function. In this work, we show that a similar construction is possible for classical...
M. Menárguez (1995)
Colloquium Mathematicae
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It is known that the weak type (1,1) for the Hardy-Littlewood maximal operator can be obtained from the weak type (1,1) over Dirac deltas. This theorem is due to M. de Guzmán. In this paper, we develop a technique that allows us to prove such a theorem for operators and measure spaces in which Guzmán's technique cannot be used.
H. Länger (1978)
Fundamenta Mathematicae
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