Banach algebra structure in Besov spaces

In this paper we give a Banach algebra structure by the Duhamel product and an invertibility criterion for Besov spaces B-p. We also describe the extended eigenvalues of the Volterra integral operator V. In the last section of the paper, motivated by the work of Karapetrovic and Mashreghi: namely, & Vert;f & lowast; g & Vert;(Aq) <= & Vert;D(1)f & Vert;(A1)& Vert;g & Vert;(Aq) for A(q)-spaces, where 1 <= q < infinity, we establish similar results by Hadamard-Bergman convolution in Besov spaces. We show that & Vert;K(g)f & Vert;(Bp )<= (pi+1)& Vert;g & Vert;(B1)& Vert;f & Vert;(Bp).