ON UNCONDITIONAL POLYNOMIAL BASES IN L(P) AND BERGMAN SPACES

In this paper we consider unconditional bases in L(p)(T), 1 <p <infini ty, p not equal 2, consisting of trigonometric polynomials. We give a lower bound for the degree of polynomials in such a basis (Theorem 3.4 ) and show that this estimate is best possible. This is applied to the Littlewood-Paley-type decompositions. We show that such a decompositi on has to contain exponential gaps. We also consider unconditional pol ynomial bases in H-p as bases in Bergman-type spaces and show that the y provide explicit isomorphisms between Bergman-type spaces and natura l sequences spaces.