On the existence of exactly one solution of integral equations in the space with a mixed norm
Bogdan Rzepecki (1975)
Annales Polonici Mathematici
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Bogdan Rzepecki (1975)
Annales Polonici Mathematici
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W. Mlak (1963)
Annales Polonici Mathematici
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Andrei K. Lerner, Kabe Moen (2013)
Studia Mathematica
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We establish several mixed bounds for Calderón-Zygmund operators that only involve one supremum. We address both cases when the part of the constant is measured using the exponential-logarithmic definition and using the Fujii-Wilson definition. In particular, we answer a question of the first author and provide an answer, up to a logarithmic factor, to a conjecture of Hytönen and Lacey. Moreover, we give an example to show that our bounds with the logarithmic factors can be arbitrarily...
Denka Kutzarova, Denny H. Leung, Antonis Manoussakis, Wee-Kee Tang (2008)
Studia Mathematica
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We study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis is said to be subsequentially minimal if for every normalized block basis of , there is a further block basis of such that is equivalent to a subsequence of . Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal, and connections with Bourgain’s ℓ¹-index are established. It is also shown that a large class of...
Horst Alzer (2000)
Czechoslovak Mathematical Journal
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Let be a real number and let be an even integer. We determine the largest value such that the inequality holds for all real numbers which are pairwise distinct and satisfy . Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value in the case and odd, and in the case and even.
Stefano Bianchini (2006)
Banach Center Publications
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In [9], the author considers a sequence of invertible maps which exchange the positions of adjacent intervals on the unit circle, and defines as Aₙ the image of the set 0 ≤ x ≤ 1/2 under the action of Tₙ ∘ ... ∘ T₁, (1) Aₙ = (Tₙ ∘ ... ∘ T₁)x₁ ≤ 1/2. Then, if Aₙ is mixed up to scale h, it is proved that (2) . We prove that (1) holds for general quasi incompressible invertible BV maps on ℝ, and that this estimate implies that the map Tₙ ∘ ... ∘ T₁ belongs to the Besov space , and its...
M. Jevtić (1985)
Matematički Vesnik
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Ronan Pouliquen (1999)
Studia Mathematica
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We prove trace inequalities of type where , under suitable hypotheses on the sequences and , with the first sequence increasing and the second bounded.
Jan Kisyński (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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Characterizations of equicontinuity and convergent sequences are given for the space of rapidly decreasing distributions and the space of slowly increasing infinitely differentiable functions.
Zhi-Wei Sun, Mao-Hua Le (2001)
Acta Arithmetica
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D. W. Hajek, I. Irizarry (1981)
Matematički Vesnik
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A. Pełczyński, H. Rosenthal (1975)
Studia Mathematica
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Richard Haydon (1972)
Publications du Département de mathématiques (Lyon)
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K. Orlov (1981)
Matematički Vesnik
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Swami Jnanananda (1936)
Časopis pro pěstování matematiky a fysiky
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P. Srivastava, K. K. Azad (1981)
Matematički Vesnik
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Ralph McKenzie (1971)
Colloquium Mathematicae
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Janusz Matkowski (1989)
Annales Polonici Mathematici
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Stephan Baier (2004)
Acta Arithmetica
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Th. Friedrich (1974)
Colloquium Mathematicae
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