• Title/Summary/Keyword: Stein spaces

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AN EXTERESION THEOREM FOR THE FOLLAND-STEIN SPACES

  • Kim, Yonne-Mi
    • Communications of the Korean Mathematical Society
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    • v.10 no.1
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    • pp.49-55
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    • 1995

  • This paper is the third of a series in which smoothness properties of function in several variables are discussed. The germ of the whole theory was laid in the works by Folland and Stein [4]. On nilpotent Lie groups, they difined analogues of the classical $L^p$ Sobolev or potential spaces in terms of fractional powers of sub-Laplacian, L and extended several basic theorems from the Euclidean theory of differentaiability to these spaces: interpolation properties, boundedness of singular integrals,..., and imbeding theorems. In this paper we study the analogue to the extension theorem for the Folland-Stein spaces. The analogue to Stein's restriction theorem were studied by M. Mekias [5] and Y.M. Kim [6]. First, we have the space of Bessel potentials on the Heisenberg group introduced by Folland [4].

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HOLOMORPHIC EMBEDDINGS OF STEIN SPACES IN INFINITE-DIMENSIONAL PROJECTIVE SPACES

  • BALLICO E.
    • Journal of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.129-134
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    • 2005

  • Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $h_L\;:\;X{\to}P(H^0(X, L)^{\ast})$ is an embedding. Choose any locally convex vector topology ${\tau}\;on\;H^0(X, L)^{\ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{\ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{\ge}1$ the restriction map ${\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})$ is surjective.

  • https://doi.org/10.4134/JKMS.2005.42.1.129 인용 PDF KSCI

WEAK HERZ-TYPE HARDY SPACES WITH VARIABLE EXPONENTS AND APPLICATIONS

  • Souad Ben Seghier
    • Journal of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.33-69
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    • 2023

  • Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝn → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

  • https://doi.org/10.4134/JKMS.j210764 인용 PDF

Generalized carleson inequality on spaces of homogeneous type

  • Yoo, Yoon-Jae
    • Journal of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.649-659
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    • 1995

  • The purpose of this paper is to generalize the Carleson inequality, which is known to play important roles in harmonic analysis. The result given here is a generalization of Coifmann, Meyer, Stein [CMS]. A similar result is shown by Deng [D].

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SOME BILINEAR ESTIMATES

  • Chen, Jiecheng;Fan, Dashan
    • Journal of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.609-620
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    • 2009

  • We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

  • https://doi.org/10.4134/JKMS.2009.46.3.609 인용 PDF KSCI