• Title, Summary, Keyword: Besov space

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THE BESOV SPACES OF M-HARMONIC FUNCTIONS

  • Lee, Jin-Kee
    • East Asian mathematical journal
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    • v.19 no.1
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    • pp.121-131
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    • 2003
  • We extend the characterization for the analytic Besov space obtained by Nowak to the invariant harmonic Besov space.

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MULTIPLIERS OF WEIGHTED BLOCH SPACES AND BESOV SPACES

  • Yang, Gye Tak;Choi, Ki Seong
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.727-737
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    • 2009
  • Let M(X) be the space of all pointwise multipliers of Banach space X. We will show that, for each $\alpha>1$, $M(\mathfrak{B}_\alpha)=M(\mathfrak{B}_{\alpha,0})=H^\infty{(B)}$. We will also show that, for each $0<{\alpha}<1$, $M(\mathfrak{B}_\alpha)$ and $M(\mathfrak{B}_{\alpha,0})$ are Banach algebras. It is established that certain inclusion relationships exist between the weighted Bloch spaces and holomorphic Besov spaces.

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NOTES ON BERGMAN PROJECTION TYPE OPERATOR RELATED WITH BESOV SPACE

  • CHOI, KI SEONG
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.3
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    • pp.473-482
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    • 2015
  • Let Qf be the maximal derivative of f with respect to the Bergman metric $b_B$. In this paper, we will find conditions such that $(1-{\parallel}z{\parallel})^s(Qf)^p(z)$ is bounded on B. We will also find conditions such that Bergman projection type operator $P_r$ is bounded operator from $L^p(B,d{\mu}_r)$ to the holomorphic Besov p-space Bs $B^s_p(B)$ with weight s.

REMARKS ON UNIQUENESS AND BLOW-UP CRITERION TO THE EULER EQUATIONS IN THE GENERALIZED BESOV SPACES

  • Ogawa, Takayoshi;Taniuchi, Yasushi
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.1007-1019
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    • 2000
  • In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

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RESOLVENT INEQUALITY OF LAPLACIAN IN BESOV SPACES

  • Han, Hyuk;Pak, Hee Chul
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.1
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    • pp.117-121
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    • 2009
  • For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

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ON A BESOV SPACE AND RADIAL LIMITS

  • Kim, Pil-Lan;Kwon, Ern-Gun;Park, Jong-Hee
    • Communications of the Korean Mathematical Society
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    • v.24 no.4
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    • pp.561-564
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    • 2009
  • A holomorphic function space in the unit disc D satisfying $\int_D|f'(z)|^p(1-|z|^2)^{p-1}dA(z)$<$\infty$ is quite close to $H^p$. The problems on the existence of the radial limits are considered for this space. It is proved that the situation for p > 2 is totally different from the situation for p $\leq$ 2.

NAVIER-STOKES EQUATIONS IN BESOV SPACE B-s,(ℝn+)

  • Jin, Bum Ja
    • Journal of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.771-795
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    • 2013
  • In this paper we consider the Navier-Stokes equations in the half space. Our aim is to construct a mild solution for initial data in $B^{-\alpha}_{{\infty},{\infty}}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1. To do this, we derive the estimate of the Stokes flow with singular initial data in $B^{-\alpha}_{{\infty},q}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1, 1 < $q{\leq}{\infty}$.