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- W2006943907 abstract "Let Bp = {f: ‖f‖ = supT⩾1 (12T) ∫−TT|f|p)1p < ∞}, 1<p<∞. Then Bp is the dual of a function algebra Aq on R (Beurling). In this paper, we study the harmonic extensions of f in Bp and in Aq, and the corresponding Hardy spaces HBp, HAq. It is shown that a parallel theory for L∞, Ll and BMO, Hl can be developed for the above pairs. In particular we prove that for 1 < q ⩽ 2, (HAq)∗ is isomorphic to the Banach space f real: ‖f‖∗,p = supT⩾112T∫−TT |f−mTf|p1p < ∞ where mTf = (12T) ∫−TTf. We also prove Burkholder, Gundy, and Silverstein's maximal function characterization for the new Hardy space HAq, 1 < q ⩽ 2." @default.
- W2006943907 created "2016-06-24" @default.
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- W2006943907 date "1989-06-01" @default.
- W2006943907 modified "2023-10-18" @default.
- W2006943907 title "Some new classes of Hardy spaces" @default.
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- W2006943907 doi "https://doi.org/10.1016/0022-1236(89)90097-9" @default.
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