A linear filter with a kernel that has zero mean could be thought of as a "DC-rejecting" filter. Is there a better or more commonly used adjective for such a filter?
In complement to Marcus, I have read the term "zero-sum": "zero-sum window", "zero-sum filter", "zero-sum kernel", the latter being more frequent. It is similar to "unit-sum windows", ie windows whose amplitudes sum to one. "Zero-average" can be found in image processing:
Further note that applying any alternative zero-average filter (in Fragmentation in the Vision of Scenes).
I however have met the term more on the opposite side: "non zero-sum" to characterize a window choose coefficients don't add to zero, which could be turned into a unit-sum window.