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a b s t r a c tThe outbreak of the 2019 novel coronavirus disease has caused more than 100,000 people to be infected and has caused thousands of deaths. Currently, the number of infections and deaths is still increasing rapidly. COVID-19 seriously threatens human health, production, life, social functioning and international relations, and has caused widespread concern around the globe. In the fight against COVID-19, geographic information systems (GIS) and big data technologies have played an important role in many aspects, including the rapid aggregation of multisource big data, rapid visualization of epidemic information, spatial tracking of COVID-19, prediction of regional transmission, identification of the spatial allocation of risk and selection of the control level, balance and management of the supply and demand of medical resources, social-emotional guidance and panic elimination, the provision of solid spatial information support for decision-making about COVID-19 prevention and control, measures formulation, and assessment of the effectiveness of COVID-19 prevention and control. GIS has developed and matured relatively quickly and has a complete technological route for data preparation, platform construction, model construction, and map production. However, for the struggle against COVID-19, the main challenge is finding strategies to adjust traditional technical methods and improve speed and accuracy to provide accurate information for rapid social management. Additionally, in the era of big data, data no longer come mainly from the government but are gathered from more diverse enterprises. As a result, the use of GIS faces difficulties in data acquisition and the integration of heterogeneous data, which requires governments, businesses, and academic institutions to jointly promote the formulation of relevant policies. At the technical level, spatial analysis methods for big data are in the ascendancy. Currently and for a long time in the future, the development of GIS should be strengthened to form a data-driven system for rapid knowledge acquisition, which signifies that GIS should be used to reinforce the social operation parameterization of models and methods, especially when providing support for social management.

Let s ∈ R, τ ∈ [0, ∞), p ∈ (1, ∞) and q ∈ (1, ∞]. In this paper, we introduce a new class of function spacesḞ s,τ p,q (R n ) which unify and generalize the Triebel-Lizorkin spaces with both p ∈ (1, ∞) and p = ∞ and Q spaces. By establishing the Carleson measure characterization of Q space, we then determine the relationship between Triebel-Lizorkin spaces and Q spaces, which answers a question posed by Dafni and Xiao in [G. Dafni, J. Xiao, Some new tent spaces and duality theorem for fractional Carleson measures and Q α (R n ), J. Funct. Anal. 208 (2004) 377-422]. Moreover, via the Hausdorff capacity, we introduce a new class of tent spaces FṪ s,τ p,q (R n+1 + ) and determine their dual spaces FẆ −s,τ/q p ,q (R n ), where s ∈ R, p, q ∈ [1, ∞), max{p, q} > 1, τ ∈ [0, q (max{p,q}) ], and t denotes the conjugate index of t ∈ (1, ∞); as an application of this, we further introduce certain Hardy-Hausdorff spaces FḢ s,τ p,q (R n ) and prove that the dual space of FḢ s,τ p,q (R n ) is justḞ −s,τ/q p ,q (R n ) when p, q ∈ (1, ∞).

Let s, τ ∈ R and q ∈ (0, ∞]. We introduce Besov-type spacesḂ s, τ p, q (R n ) for p ∈ (0, ∞] and Triebel-Lizorkin-type spacesḞ s, τ p, q (R n ) for p ∈ (0, ∞), which unify and generalize the Besov spaces, Triebel-Lizorkin spaces and Q spaces. We then establish the ϕ-transform characterization of these new spaces in the sense of Frazier and Jawerth. Using the ϕ-transform characterization ofḂ s, τ p, q (R n ) andḞ s, τ p, q (R n ), we obtain their embedding and lifting properties; moreover, for appropriate τ , we also establish the smooth atomic and molecular decomposition characterizations ofḂ s, τ p, q (R n ) andḞ s, τ p, q (R n ). For s ∈ R, p ∈ (1, ∞), q ∈ [1, ∞) and τ ∈ [0, 1 (max{ p, q}) ], via the Hausdorff capacity, we introduce certain Hardy-Hausdorff spaces BḢ s, τ p, q (R n ) and prove that the dual space of BḢ s, τ p, q (R n ) is justḂ −s, τ p , q (R n ), where t denotes the conjugate index of t ∈ (1, ∞).