• Korean Journal of Mathematics
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• 제16권1호
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• pp.85-90
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• 2008

We consider Fourier multiplier operators whose symbols satisfy a generalization of $H{\ddot{o}}rmander^{\prime}s$ condition and establish their Sobolev-type mapping properties on the homogeneous Besov-Lipschitz spaces by making use of a continuous characterization of Besov-Lipschitz spaces. As an application, we derive Sobolev-type imbedding theorem.

• 대한수학회지
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• 제43권2호
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• pp.283-296
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• 2006

In this paper we weaken the kernel conditions of bilinear Calderon-Zygmund operators and prove boundedness on Besov spaces.

• 대한수학회지
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• 제36권6호
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• pp.1075-1090
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• 1999

This paper deals with Littlewood-Paley type estimates of the Besov spaces {{{{ { B}`_{p,q } ^{$\alpha$ } }}}} on the d-dimensional unit cube for 0< p,q<$\infty$ by two certain classes. These classes are including biorthogonal wavelet systems or dual multiscale systems but not necessarily obtained as the dilates or translates of certain fixed functions. The main assumptions are local supports of both classes, sufficient smoothness for one class, and sufficiently many vanishing moments for the other class. With these estimates, we characterize the Besov spaces by coefficient norms of decompositions with respect to biorthogonal wavelet systems on the cube.

• 충청수학회지
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• 제23권4호
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• pp.773-784
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• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• 충청수학회지
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• 제36권2호
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• pp.87-91
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• 2023

It is concerned with the size of bounded functions in Besov spaces. It reports that every closed subspace consisted with bounded functions in Besov spaces B^s_p,p(𝕋^d) (s < 0) is finite dimensional.

• 대한수학회논문집
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• 제36권4호
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• pp.651-669
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• 2021

In this paper, we investigate some basic results on the slice regular Besov spaces of hyperholomorphic functions on the unit ball 𝔹. We also characterize the boundedness, compactness and find the essential norm estimates for composition operators between these spaces.

• 대한수학회보
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• 제60권3호
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• pp.649-657
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• 2023

In this paper, we give new necessary and sufficient conditions for the compactness of composition operator on the Besov space and the Bloch space of the unit ball, which, to a certain extent, generalizes the results given by M. Tjani in [10].

• East Asian mathematical journal
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• 제19권1호
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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.

• 대한수학회보
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• 제61권2호
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• pp.529-540
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• 2024

In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear Hörmander class $BS^{m}_{1,1}$ in variable Triebel-Lizorkin spaces and variable Besov spaces.

• 충청수학회지
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• 제22권4호
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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.