Calderón–Zygmund operators on multiparameter Lipschitz spaces of homogeneous type

The purpose of this paper is to establish a necessary and sufficient condition for the boundedness of general product singular integral operators introduced by Han, Li and Lin [Y. Han, J. Li and C.-C. Lin, Criterion of the L 2 L^{2} boundedness and sharp endpoint estimates for singular integral operators on product spaces of homogeneous type, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 2016, 3, 845–907] on the multiparameter Lipschitz spaces of homogeneous type M ~ = M 1 × ⋯ × M n {\tilde{M}=M_{1}\times\cdots\times M_{n}} . Each factor space M i {M_{i}} , 1 ≤ i ≤ n {1\leq i\leq n} , is a space of homogeneous type in the sense of Coifman and Weiss. These operators generalize those studied by Journé on the Euclidean space and include operators studied by Nagel and Stein on Carnot–Carathéodory spaces. The main tool used here is the discrete Littlewood–Paley–Stein theory and almost orthogonality together with a density argument for the product Lipschitz spaces in the weak sense.

Boundedness of Some Paraproducts on Spaces of Homogeneous Type

Let (X,d,μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this article, the author develops a partial theory of paraproducts {Πj}j=13 defined via approximations of the identity with exponential decay (and integration 1), which are extensions of paraproducts defined via regular wavelets. Precisely, the author first obtains the boundedness of Π3 on Hardy spaces and then, via the methods of interpolation and the well-known T(1) theorem, establishes the endpoint estimates for {Πj}j=13. The main novelty of this paper is the application of the Abel summation formula to the establishment of some relations among the boundedness of {Πj}j=13, which has independent interests. It is also remarked that, throughout this article, μ is not assumed to satisfy the reverse doubling condition.

The structure of the oropharyngeal genus Candida fungi community in HIVinfected patients

At the present time virtually no data are available about the structure of the genus Candida fungus able to target HIV-infected patients and serve as an etiological factor of candidiasis. The aforementioned shaped the aim of the study: to examine structure of the Candida genus community colonizing the oropharynx in HIV-infected patients with clinical manifestations of oropharyngeal candidiasis. There was conducted a microbiological study of the oropharynx in 31 HIV-infected patients (51.6% males and 48.4% females) with clinical manifestations of oropharyngeal candidiasis treated at Moscow Infectious Clinic No. 2 inpatient department in the years 2015–2017. We confirmed the diversity of the oropharyngeal Candida spp. community found in HIV-infected patients. Total 52 isolates of the genus Candida were isolated. C. albicans dominated in 57.7% cases, whereas C. glabrata prevailed (21.1%) among non-albicans species. Minor components were represented by C. tropicalis (11.5%) and C. krusei (9.6%). C. albicans and C. glabrata were sensitive to polyenes, whereas minor community components — to itroconazole and clotrimazole. The vast majority of fungal strains were resistant to fluconazole. The genus Candida community reveals a unique architecture so that any member may exist in the oropharyngeal biotope of HIV-infected patients as a monoculture or in association: homogeneous, consisting of a single species strains, or heterogeneous, formed by several species. Candida fungi in 18 patients (58.1%) were isolated as a monoculture, whereas in 13 (41.9%) subjects — in association consisting of 34 isolates (65.4% of total number), of which 16 (30.8%) and 18 (34.6%) were isolated from homogeneous and heterogeneous associations, respectively. There were identified 9 two-component associations (69.2%), and 4 (30.8%) consisting of three or more components. It turned out that pattern of the examined community was mainly determined by species composition that agrees with previous data. Most common associations were presented by C. krusei (100%) and C. albicans (73.3%). Upon that, most often C. albicans (72.7%) formed a homogeneous type of associations. Sensitivity of Candida fungi to antimycotic drugs also depended on the architecture of related community. C. albicans isolates in heterogeneous associations revealed a wide range of resistance acquired by contact with non-albicans species.