On the quantitative coarse Baum-Connes conjecture with coefficients

In this paper, we introduce the quantitative coarse Baum-Connes conjecture with coefficients (or QCBC, for short) for proper metric spaces which refines the coarse Baum-Connes conjecture. And we prove that QCBC is derived by the coarse Baum-Connes conjecture with coefficients which provides many examples satisfying QCBC. In the end, we show QCBC can be reduced to the uniformly quantitative coarse Baum-Connes conjecture with coefficients of a sequence of bounded metric spaces.
Comment: 30 pages; all comments are welcome! arXiv admin note: text overlap with arXiv:2410.11662