A Note on Hilberts Operator

نویسنده

  • H. KOBER
چکیده

LEMMA L 1 When Kp< oo, then &fis a continuous (bounded) linear transformation with both domain and range Lp( — <*> , oo ), and § 2 / = — ƒ. LEMMA 2. Whenf(t)ÇzLi(— <*>, oo), then §ƒ exists for almost all x in ( — oo , co ), but does not necessarily belong to Li(a, b), where a, b are arbitrary numbers(— oo ^a<b^ oo) ; however (l+x)~\ &f\ÇzLi(— oo , co) when 0<q<l. When f and ^f belong to Li(— oo , oo), then § 2 / = —ƒ.

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تاریخ انتشار 2007