“…It is well known that the classical Hilbert-type inequalities are usually constructed in the first quadrant. In recent years, with more and more researchers participating in the study of Hilbert-type inequalities, some researchers extended the range of variables to the whole plane and established many valuable new results (see [7,16–18,21,33,37,41]). Inspired by the related results in these literatures, we will construct the following new inequalities: where , , , and .…”