Linear and Complex Analysis Problem Book: 199 Research by J. Bourgain, A. Pełczyński, I. A. Komarchev (auth.), Victor

By J. Bourgain, A. Pełczyński, I. A. Komarchev (auth.), Victor P. Havin, Sergei V. Hruščëv, Nikolai K. Nikol'skii (eds.)

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A. KO~H~IEB) B. M. M. , M i 1 - s p h e r i c a l s e c t i o n s of c o n v e x 53-94. CCCP, 198904, HeTpo~Bopen, ~M6~OTeqHa~ ~ . 4. old Let A be the B~n~ch space of all functions continuous in ~ ~ and analytic in ~ , equipped with the supremum norm and let H~ me the Hardy space. W consider A as a subspace of C(~) and HI as a subspace of ~I(~) ~ We would like %o know the relation between finite dimensional subspaces and finite dimensional operators in and those in O(~) . This question is of importance in the theory of the Banach space A .

1979, 33, 109-143. 2. M. E. Verallgemeinerte Funktionen II, III. VEB Deutscher Verlag der Wissenschaften, Berlin 1962. 3. H a s i i n g e r ~z P. and M e y e r approv~mAtion and interpolation. 4. K o t h e M. Abel - Goncarov - Preprint. G. Topologische lineare Raume. Berlin, Heidelberg~ New York, Springer Verlag, 1966. 5. M a r t i n e a u A. Equations diff~rentielles d'ordre infini. - B u l l . S o c . M a t h . 6. C. de France, 1967, 95, 109-154. H~epRocT~ ~ ~ p ~ e . O-Ba, C~O~CTBa npocTpa~cTB I960, 9, 817--328.

13. B e u r g a i n J. On the primsrity in H ~ -spaces. - Preptint. 6. old SPACES OF HARDY TYPE A Banach Space E of measurable functions on [ 0 , ~ ] is called a symmetric (or rearrangement invariant) space iff the norm of E is monotone and any two equimeasurable functions have equal norms. ( ~ ] , chapter 2). The ~ -spaces ( ~ p ~ ) , the Orlicz spaces and the Lerentz spaces can serve as examples. Remind that if the function is non-decreasing and concave on [ 0 , ~ ] , ~ ( 0 ) ~ 0 , then the Lorentz space A(~) consists of functions ~ such that 4 o where ~ * is the function non-increasing on[0,~g] and equimeasurable with ~ .

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