Operators on Spaces of Analytic Functions Belonging to L Ž1, .

Let H be a separable Hilbert space and K be the ideal of compact operators on H. A T K is said to be in L Ž1, . if nŽT. OŽlog n. for n 2 or, equivalently, supN 2Ž1 log N.Ý1N nŽT. , where nŽT. are the singular values Žeigenvalues of T ŽT*T.1 2 .. In this paper, we will give geometric conditions on several classes of operators, including Hankel and composition operators, belonging to L Ž1, .. Specifically, we will show that the function space characterizing the symbols of these operators is a nonseparable Banach space which lies strictly between B1ŽD.and all the other holomorphic Besov spaces BpŽD.Žp 1..