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Weighted Harmonic Bergman functions on Half-Spaces
구형운,남계숙,이흥수 대한수학회 2005 대한수학회지 Vol.42 No.5
On the setting of the upper half-space H of the Euclidean n-space, we study weighted harmonic Bergman functions as follows. First, we define the fractional derivatives of some functions defined on H. Next, we find the explicit formula for weighted Bergman kernel through the fractional derivative of the extended Poisson kernel and then we give the size estimates for derivatives of this kernel.
Holomorphic mean Lipschitz functions on the unit ball of Cn
권언근,조홍래,구형운 대한수학회 2013 대한수학회지 Vol.50 No.1
On the unit ball of Cn, the space of those holomorphic functions satisfying the mean Lipschitz condition∫10 wp(t,f)q dt/t1+αq< ∞ characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ωp(t, f) denotes the Lp modulus of continuity defined in terms of the unitary transformations of Cn.