  We constructively determine the Pietsch measure of the 2-summing
multiplication operator
  \[\mathcal{M}_u:\ell^{\infty} \rightarrow H^p, \quad (\varphi_I) \mapsto \sum
\varphi_Ix_Ih_I. \] Our construction of the Pietsch measure for the
multiplication operator $\mathcal{M}_u$ involves the Haar coefficients of $u$
and its atomic decomposition.
