  This article extends the celebrated sewing lemma to multi-parameter fields on
hyper cubes. We use this to construct Young integrals for multi-parameter
H\"older fields on general domains [0,1]^{k} with k>=1. Moreover, we show
existence, uniqueness and stability of some particular types of hyperbolic
SPDE's driven by space-time H\"older noise in a Young regime
  This article replaces the article "Rough Integration for Fields - with
applications to stochastic hyperbolic PDE's". Due to errors in the first
article in the section on rough fields, we have decided to divide this article
into two parts. The first, is dealing with extending the sewing lemma to
general multi parameter functions as well as hyperbolc equations driven by
multiparameter fields in a Young regime. The next article will come later and
study the rough path type framework implied by the extended sewing lemma.
