Calderón's reproducing formula for Hankel convolution

where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferential operators related to the Bessel operator. Pathak and Dixit [7] exploited Hankel convolution in their study of Bessel wavelet transforms. In what follows, we give definitions and results related to the Hankel convolution [5] to be used in the sequel. Let γ be a positive real number. Set