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Yu. A. Farkov 《Mathematical Notes》2000,68(2):248-254
Suppose thatB
R
d
is a ball of radiusR in ℂ
d
and σ is the standard measure on the unit sphere in ℂ
d
. ForR>1, 1≤p≤∞, and for the natural numbersl, d, byH
R
0
(l, p, d) we denote the class of functionsf holomorphic inB
R
d
and such that in the homogeneous polynomial expansion of the firstl summands the zero and radial derivatives of orderl belong to the closed unit ball of the Hardy spaceH
p
(B
R
d
). In this paper an asymptotic formula for the ε-entropy of the classH
R
0
(l, p, d) in the spacesL
p
(σ), 1≤p<∞, and
is obtained.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 286–293, August, 2000. 相似文献
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