p-Summing Multiplication Operators, dyadic Hardy Spaces and atomic Decomposition

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

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