The characterizations of (Aq(U))

Abstract

For q > J Be rs. Iefin es a Banach s pa ce A,,(U) = {/EH(U) 1 I.1 /(1I)1(1-lnl")q~2dxdy < 00 } a nd s how s th a t a ny bou nd e d lin ea r fun c tion al \ on A ,,(U) may b e rep!"esen ted a,; "(I) = j l(n)C(u)(1-,. InI2)2q ~ 2dxdy where CEB ,,(V) = {hE H (U) 1 s up Ih (I1)I(1-lul,)q < co } and is uniqu e. T hi s work is IIE/ ' do n e in [1 p. Duren , R o mbe rg, a nd S hi e ld s. purs uant to th e ir work 4Jn H" for p < l , d efi ne a B a n ac h s pa ce B"(P < 1) = {/E H (V) I J,2~J,, ' I/(rei!J)I (l-r) I /" 'drd(J

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(Aq(U))的表征

For q > J Be rs Iefin es a·s, a,, (U) = (/ EH (U) 1。1 / (ii) (1-lnl”)q ~ 2dxdy < 00) nd s th知识o t a纽约布nd和d / r的c, \ on a、b (U) may和代表ted宽松!”,;“(I) = j l(n)C(u)(1-，InI2) 2q ~ 2dxdy where CEB,, (V) = (hE H (U) 1 s up H (1) I (1-lul) q <) and is uniqu e . T hi s work is IIE / ' do号和[1 p . Duren、R或mbe rg、nd s hi ld和s . purs uant th和ir work 4Jn H”for p < l, d efi B a n ac H s, B”(p < 1) = (/ H (V) 2 ~ J, J, I / J (!) (l-r) /“’drd (J < oo)。Th 80万吨s知识Th a i bllund和d / r功能(' t . no, a lin) B "莱拉y be uniqu和14.1 noe nt d as”(f) = lim f’j。(! J) g (eiO) dlJ whe r - + J或国王(i) 1、(eiO) = (111) _, (ii) / ea = (H (U) 1 g is ntinu llus lin V)和杜松子酒(i) a nd年息12 5t d e . ti of g, is在林业、l / s =(嘿嘿(阿拉伯联合酋长国)(reiO) =或(l-r)”-(和国王(y = l / p-1I where II < I / p <二+ 1,Sll¥或。If / p = II + l, th和ndition s g s: gEA, gin-ilEA = (hdl (V) l h”(reiO) = 0«(1-r) ~)。在[2J]， *在Ihi s paper中。是的。1 /p= q, l /p= q, l /p= n C a lld·“(保密< 1)where are C4J ns tant s, A’n + 1“'”或“thi。(s号房屋q = p / l is a r . int ege Th和Th eo m is s ghtl y rliffere nl他们if q is nol an ege r .) (III) Q-2dXdy 0-lu I2 = . l ....J I 1/1(1-r2) q-2rdrdO ~ max 0, 21 -2) (27T ..)

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