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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M. Jevtić (1985)
Matematički Vesnik
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J. Korevaar (1986)
Matematički Vesnik
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W. Mlak (1963)
Annales Polonici Mathematici
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Xiangling Zhu (2011)
Annales Polonici Mathematici
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Let H(B) denote the space of all holomorphic functions on the unit ball B of ℂⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. We study the integral-type operator , f ∈ H(B). The boundedness and compactness of from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied
Denny H. Leung, Wee-Kee Tang (2006)
Studia Mathematica
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We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space : (1) Every block subspace of X contains an -spreading model, (2) The Bourgain ℓ¹-index for any block subspace Y of X, (3) and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these...
Diana D. Jiménez S., Lino F. Reséndis O., Luis M. Tovar S. (2014)
Banach Center Publications
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Following the line of Ouyang et al. (1998) to study the spaces of holomorphic functions in the unit ball of ℂⁿ, we present in this paper several results and relations among , the α-Bloch, the Dirichlet and the little spaces.
Nabil Ourimi (2002)
Annales Polonici Mathematici
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The purpose of this paper is to prove that proper holomorphic self-mappings of the minimal ball are biholomorphic. The proof uses the scaling technique applied at a singular point and relies on the fact that a proper holomorphic mapping f: D → Ω with branch locus is factored by automorphisms if and only if is a normal subgroup of for some and .
Yu-Xia Liang, Chang-Jin Wang, Ze-Hua Zhou (2015)
Annales Polonici Mathematici
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Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator on H() is defined by . We investigate the boundedness and compactness of induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.
Anahit Harutyunyan, Wolfgang Lusky (2010)
Studia Mathematica
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We study the spaces where Ω is a disc with radius R and μ is a given probability measure on [0,R[. We show that, depending on μ, is either isomorphic to l₁ or to . Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere.
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...
Le Mau Hai, Tang Van Long (2002)
Studia Mathematica
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The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property for the dual space of the space of germs of holomorphic functions on that compact set.
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...
Ting Guo, Zhiming Feng, Enchao Bi (2021)
Czechoslovak Mathematical Journal
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We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain . The generalized Fock-Bargmann-Hartogs domain is defined by inequality , where . In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic self-mapping of the generalized Fock-Bargmann-Hartogs domain becomes a holomorphic automorphism if and only if it keeps the function invariant.
Wolfgang Lusky (2006)
Studia Mathematica
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Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of and investigate some isomorphism classes of where v is a given radial weight function. Our main results show that, without any further condition on v, there are only two possibilities for Hv, namely either or , and at least two possibilities for hv, again and . We also discuss many new examples of weights.
Philippe Eyssidieux, Carlos Simpson (2011)
Journal of the European Mathematical Society
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Let be a compact Kähler manifold, be a base point and be the monodromy representation of a -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at and a variation of mixed Hodge structures whose monodromy is the universal deformation of .
Marek Jarnicki, Peter Pflug (2003)
Annales Polonici Mathematici
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Let be a pseudoconvex domain and let be a locally pluriregular set, j = 1,...,N. Put . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001]. ...
Е.М. Кузнецова (1986)
Trudy Geometriceskogo Seminara
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B. Platynowicz (1980)
Matematički Vesnik
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Ngaiming Mok (2012)
Journal of the European Mathematical Society
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We study the extension problem for germs of holomorphic isometries up to normalizing constants between bounded domains in Euclidean spaces equipped with Bergman metrics on and on . Our main focus is on boundary extension for pairs of bounded domains such that the Bergman kernel extends meromorphically in to a neighborhood of , and such that the analogous statement holds true for the Bergman kernel on . Assuming that and are complete Kähler manifolds, we prove that...
Piotr Jakóbczak (1993)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Let be a domain in . Given , set . If is a holomorphic and square-integrable function in , then the set of all such that is not square-integrable in has measure zero. We call this set the exceptional set for . In this Note we prove that whenever there exists a holomorphic square-integrable function in the unit ball in such that is the circle .
Andriy Bandura, Tetyana Salo, Oleh Skaskiv (2024)
Mathematica Bohemica
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For a given direction we study non-homogeneous directional linear higher-order equations whose all coefficients belong to a class of joint continuous functions which are holomorphic on intersection of all directional slices with a unit ball. Conditions are established providing boundedness of -index in the direction with a positive continuous function satisfying some behavior conditions in the unit ball. The provided conditions concern every solution belonging to the same class...