  In this paper, we extend the quadratic phase Fourier transform of a complex
valued functions to that of the quaternion valued functions of two variables.
We call it the quaternion quadratic phase Fourier transform (QQPFT). Based on
the relation between the QQPFT and the quaternion Fourier transform (QFT) we
obtain the sharp Hausdorff-Young inequality for QQPFT. We define the short time
quaternion quadratic phase Fourier transform (STQQPFT) and explore some of its
properties including inner product relation and inversion formula. We find its
relation with that of the 2D quaternion ambiguity function and the quaternion
Wigner-Ville distribution associated with QQPFT and obtain the Lieb's
uncertainty and entropy uncertainty principles for these three transforms.
