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Agglomeration of the industry significantly impacts economic performance and environmental sustainability. In line with its strategic context of striving to achieve carbon reduction targets, China is making efforts to optimize the producer services landscape to reduce carbon emissions. Understanding the spatial correlation between industrial agglomeration and carbon emissions is particularly crucial against this background. Based on POI and remote sensing data of China’s Yangtze River Economic Belt (YREB), the paper adopts the mean nearest neighbor analysis, kernel density analysis, and standard deviation ellipse to portray the agglomeration of producer services. Then uses Moran's I to present the spatial distribution characteristics of carbon emissions. Accordingly, the spatial heterogeneity of producer services agglomeration and carbon emissions is showed using the Geographic detector so as to provide strong support for industrial structure optimization and sustainable development. Here are some of the conclusions drawn from the study: (1) Producer services are a significant state of agglomeration in the provincial capitals and some central cities, with similar agglomeration patterns. (2) Carbon emissions exhibits significant spatial aggregation characteristics, with the spatial distribution pattern of "High west–Low east". (3) Wholesale and retail services industry is the primary risk factor that causes spatial differentiation of carbon emission intensity, "leasing and business services industry-wholesale and retail services industry" is the key interaction factor of the spatial differentiation. (4) Carbon emissions shows a downward trend followed by an upward trend as producer services agglomeration increases.

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The Beijing–Tianjin–Hebei urban agglomeration (BTHUA) has experienced ecological and environmental issues due to its rapid development and expansion, including air and water pollution. Examining inter-regional plans for sustainable and low-carbon sustainable development is crucial and practical for achieving ecological balance among regions and fostering the BTHUA’s commitment to collaborative innovation. This study applies the three-stage data envelopment analysis (DEA) model to 13 cities in the BTHUA between 2007 and 2020 to compute the sustainable and low-carbon development efficiency (SLE) and index, and then constructs a fundamental model of urban agglomeration growth. In this study, MATLAB software was used to predict the general evolution trend and development curve for the BTHUA’s low-carbon and green economy development. The results of the study indicate (1) the efficiency of sustainable and low-carbon development in the BTHUA has a wave-like ascending tendency, generating an overall development pattern that is centred on core cities and eventually descends toward the periphery. (2) In recent years, coordination between sustainable and low-carbon development indices and development levels within BTHUA has largely improved; however, a changing nonlinear relationship exists between the sustainable and low-carbon efficiency index and development levels. (3) The BTHUA’s sustainable and low-carbon development curve displays a tendency that is consistent with the function model’s anticipated evolution trend.

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