An extension of the Hardy-Littlewood inequality
An extension of the Hardy-Littlewood inequality
An extension of the Hardy-Littlewood inequality
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<strong>An</strong> Extens i on <strong>of</strong> <strong>the</strong> <strong>Hardy</strong>- Li t t lewood I ne guality 57<br />
D ( b S) cD ( p ~ q ) s i n c e Sn( q lf)~ S n (s ~f) . On <strong>the</strong> o<strong>the</strong>r han d if<br />
! ( z)=r.b a 2 " wher e III 1l = zn U - p +p/ s )<br />
n<br />
n<br />
t hen fED(p ~q ) . wh i l e ftf. D ( l ~ 8 ) . Thus o ur resu l t i mprov e s <strong>the</strong> Ho l l a nd <br />
Twomey <strong>the</strong>orem.<br />
Note that a l l inclus i ons whic h oc cur i n The or em 1 a r e prope<br />
r . For e xamp l e , i f<br />
2 2 "<br />
! (z) =r. n- z<br />
<strong>the</strong> n fEli "" and f$ D (p ~q) f or zcpc» a nd p-! +q - l
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