By J. Bourgain, A. Pełczyński, I. A. Komarchev (auth.), Victor P. Havin, Sergei V. Hruščëv, Nikolai K. Nikol'skii (eds.)
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Extra resources for Linear and Complex Analysis Problem Book: 199 Research Problems
Example text
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 ~ .