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The Hardy-Morrey spaces related to Laplace-Bessel differential equations areintroduced in terms of maximal functions. The atomic decomposition theory whichhas the same cancellation properties of the$H^{p}_{\Delta_{\nu}}(\mathbb{R}^{n}_{+})$ Hardy spaces is established.

Different approach to the decomposition theory of $HM^p_{q,{\Delta_{\nu}}}$ Hardy-Morrey spaces