Unboundedness of the Bergman projections on \(L^p\) spaces with exponential weights. (English) Zbl 1077.47020
The paper shows that the Bergman projection is unbounded on \(L^p(D,wdA)\) for \(p\not=2\), where \(D\) is the unit disk, \(dA\) is the area measure on \(D\), and
\[
w(z)=(1-| z| ^2)^Ae^{-B/(1-| z| ^2)^\alpha}
\]
is a weight function on \(D\). Here the Bergman projection means the orthogonal projection from \(L^2(D,wdA)\) onto the Bergman space \(L^2_a(D,wdA)\) consisting of analytic functions in \(L^2(D,wdA)\).
Reviewer: Kehe Zhu (Albany)
MSC:
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
