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Abstract: In this paper, we study an analogy of the heat operator to the skew-holomorphic Jacobi form case. Using this, we prove Bol’s identity for skew-holomorphic Jacobi forms on Hn ×Mj,n(C). This induces a map from skew-holomorphic Jacobi forms of weight −k + n+j−1 2 to those of weight k + n+j−1 2 + 2. When n = j = 1, this map extends to skew-holomorphic harmonic Maass-Jacobi forms. In this case, we prove Zagier-type duality between Fourier coefficients of harmonic Maass-Jacobi forms and Fourier coefficients of weakly skew-holomorphic Jacobi forms.

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