Integral refinable operators exact on polynomials

We study integral refinable operators of integral type exact on polynomials of even degree constructed by using refinable B-bases of GP type. We prove a general theorem of existence and uniqueness. Then we study the L p -norm of these operators and we give error bounds in approximating functions and their derivatives belonging to suitable classes. Numerical results and comparisons with other quasi-interpolatory operators having the same order of exactness on polynomial reproduction are presented.