×

Analytic multipliers of Bergman spaces. (English) Zbl 0589.46042

The author provides his results contained in his doctorial dissertation, through seven sections in this paper. Sections 1 and 2 contain basics and introduction with some examples, on unbounded multipliers from \(L^ 2_ a(D)\) to \(L^ 2(D)\). Section 3 deals with propositions on harmonic multipiers of \(L^ p_ a(W)\) to \(L^ p(W)\). A lemma is exhibited in order to classify the harmonic multipliers of \(L^ 2_ a(D')\) to \(L^ 2(D')\) through section 4. Similar results are presented in the remaining sections.
The author gives a partial solution to the question that whether the sub- harmonic multipliers of \(L^ 2_ a(D)\) to \(L^ 1(D)\) be in \(L^ 2(D)\). The author also presents the result of D. H. Luecking in the paper as follows: The sub-harmonic function 1/\(\sqrt{1-| z|}\) on D does not multiply \(L^ 2_ a(D)\) to \(L^ 1(D)\).
Reviewer: S.Sridhar

MSC:

46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
30H05 Spaces of bounded analytic functions of one complex variable
PDFBibTeX XMLCite
Full Text: DOI