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The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA

Joseph CimaRaymond Mortini — 1995

Studia Mathematica

It is shown that the Bourgain algebra A ( ) b of the disk algebra A() with respect to H ( ) is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to H ( ) , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is A ( ) b .

Growth estimates for generalized factors of H p spaces

Joseph A. CimaAngeliki KazasMichael I. Stessin — 2003

Studia Mathematica

With φ an inner function and M φ the multiplication operator on a given Hardy space it is known that for any given function f in the Hardy space we may use the Wold decomposition to obtain a factorization of the given f (not the Riesz factorization). This new factorization has been shown to be useful in the study of commutants of Toeplitz operators. We study the smoothness of each factor of this factorization. We show in some cases that the factors lie in the same Hardy space (or smoothness class)...

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