This paper proposes RAPNet, a novel CNN-based architecture, to address the pansharpening problem of combining high-resolution panchromatic (PAN) images with low-resolution multispectral (MS) images to produce a high-resolution fused image. RAPNet performs content-adaptive convolutions, using receptive-field adaptive pansharpening convolutions (RAPConv), which adjust receptive field sizes according to spatial position. Furthermore, it utilizes a pansharpening dynamic feature fusion (PAN-DFF) module that integrates an attention mechanism to optimize the trade-off between spatial detail enhancement and spectral fidelity. Experimental results using public datasets demonstrate that RAPNet outperforms existing methods in both quantitative and qualitative evaluations, and the effectiveness of the proposed adaptive components is further validated through ablation studies.