PM2.5, which refers to fine particles with an equivalent aerodynamic diameter of less than or equal to 2.5 µm, can not only affect air quality but also endanger public health. Nevertheless, the spatial distribution of PM2.5 is not well understood in data-poor regions where monitoring stations are scarce. Therefore, we constructed a random forest (RF) model and a bagging algorithm model based on ground-monitored PM2.5 data, aerosol optical depth (AOD) and meteorological data, and auxiliary geographical variables to accurately estimate the spatial distribution of PM2.5 concentrations in Xinjiang during 2015–2020 at a resolution of 1 km. Through 10-fold cross-validation (CV), the RF model and bagging algorithm model were verified and compared. The results showed the following: (1) The RF model achieved better model performance and thus can be used to estimate the PM2.5 concentration at a relatively high resolution. (2) The PM2.5 concentrations were high in southern Xinjiang and low in northern Xinjiang. The high values were concentrated mainly in the Tarim Basin, while most areas of northern Xinjiang maintained low PM2.5 levels year-round. (3) The PM2.5 values in Xinjiang showed significant seasonality, with the seasonally averaged concentrations decreasing as follows: winter (71.95 µg m−3) > spring (64.76 µg m−3) > autumn (46.01 µg m−3) > summer (43.40 µg m−3). Our model provides a way to monitor air quality in data-scarce places, thereby advancing efforts to achieve sustainable development in the future.

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In this paper, we establish sharp maximal function inequalities for the Toeplitz-type operator associated with the singular integral operator with a variable Calderón-Zygmund kernel. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces.

In this paper, the boundedness of certain multilinear operator related to the multiplier operator from Lebesgue spaces to Orlicz spaces is obtained.