Some eigenvalue estimates for wavelet related Toeplitz operators

By a straightforward computation we obtain eigenvalue estimates for Toeplitz operators related to the two standard reproducing formulas of the wavelet theory. Our result extends the estimates for Calderón-Toeplitz operators obtained by Rochberg in [R2]. In the first section we recall two standard reproducing formulas of the wavelet theory, we define Toeplitz operators and discuss some of their properties. The second section contains precise statements of our results and their proofs. At the end of the second section we include some comments about the range of applicability of our estimates.