Lebesgue constant for the Strömberg wavelet

Abstract

Let S denote the Strömberg wavelet in L 2( R) and P s,n (s∈ Z, n∈ Z∪{∞}) , the orthogonal projection onto the space spanned by the functions 2 r/2 S(2 r t− m), where r⩽ s, m< n+1 (i.e. P s, n are partial sums for the orthonormal wavelet basis generated by S). We show that the maximum of the norms of the extensions of the operators P s, n onto L ∞( R) is equal to 2+(2− 3 ) 2 .