Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex

We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors' recent result obtained for a Euclidean sphere of arbitrary dimension. Furthermore, similar heat kernel bounds are shown in the context of classical Jacobi expansions, on a ball and on a simplex. These results are more precise than the qualitatively sharp Gaussian estimates proved recently by several authors.Comment: 16 page

Sharp estimates of the spherical heat kernel

We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension. This solves a long-standing open problem.Comment: 9 pages, to appear in J. Math. Pures Appl. (9

On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings

We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, $g$-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes type. By means of the general Calder\'on-Zygmund theory we prove that these operators are bounded on weighted $L^p$ spaces, $1 < p < \infty$, and from weighted $L^1$ to weighted weak $L^1$. We also obtain similar results for analogous set of operators in the closely related multi-dimensional Laguerre-symmetrized framework. The latter emerges from a symmetrization procedure proposed recently by the first two authors. As a by-product of the main developments we get some new results in the multi-dimensional Laguerre function setting of convolution type

Riesz-Jacobi transforms as principal value integrals

We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders express as principal value integrals against kernels having non-integrable singularities on the diagonal. On the other hand, we show that the Riesz-Jacobi transforms of even orders are not singular operators. In fact they are given as usual integrals against integrable kernels plus or minus, depending on the order, the identity operator. Our analysis indicates that similar results, existing in the literature and corresponding to several other settings related to classical discrete and continuous orthogonal expansions, should be reinvestigated so as to be refined and in some cases also corrected.Comment: 30 page

Kur yra gėjus: erdvės pavadinimai lenkiškuose zinuose ir žurnaluose

The circulation of zines and the first gay magazines is treated as one of the most important elements of alternative communication. Zines created an opportunity for gay communities to communicate, which in the 1980s and 1990s was clearly difficult, and in small towns even impossible (communication via the Internet began to be discussed only in the mid-1990s). That is why the press became a kind of gay news agency, a platform for the exchange of information and experiences, and, most importantly, a record of the language of the non-heterosexual communities at the time. The aim of the article is to present a fragment of their reality: the space written in gay magazines, their names and the codes and behaviors associated with them. In my research, I have referred to M. Foucault’s heterotopia and the subversion of space. In this way, I have drawn a linguistic map of the space of gay culture.Zinų ir pirmųjų gėjams skirtų žurnalų sklaida yra vienas svarbiausių alternatyvios komunikacijos elementų. Zinai sukūrė galimybę bendrauti gėjų bendruomenėse, nes XX a. devintą ir dešimtą dešimtmečius tai buvo akivaizdžiai sudėtinga, o mažose gyvenvietėse veik neįmanoma (apie bendravimą internetu pradėta kalbėti tik paskutinio dešimtmečio viduryje). Todėl spauda tapo savotiška gėjų naujienų agentūra, informacijos ir patirties mainų platforma, o svarbiausia&nbsp;– tuometinių neheteroseksualių asmenų bendruomenių kalbos įrašu. Straipsnio tikslas&nbsp;– pristatyti jų tikrovės fragmentą: gėjų žurnaluose aprašomas erdves, jų pavadinimus ir su jais susijusius kodus bei elgseną. Savo tyrime remiuosi M. Foucault heterotopija ir erdvės subversija. Taip atskleidžiu lingvistinį gėjų kultūros erdvės žemėlapį

The effect of human capital on labour productivity of farms in Poland

This study aims to determine the relationship between total, average and marginal human factor productivity and the level of education of a farm manager in Poland. The study was carried out based on unit empirical data from the monitoring of the Polish Farm Accountancy Data Network (FADN) and covered the four Polish FADN macro-regions: Pomorze & Mazury, Wielkopolska & Śląsk, Mazowsze & Podlasie and Małopolska & Pogórze. The study involved the Cobb-Douglas production function method. Using the relationship between total production (in PLN) of a farm and the aggregated production factors such as total labour input in AWU (Annual Work Unit), area of arable land (ha) and fixed assets (PLN), labour productivity was determined based on the level of education of the farm manager. The results indicate that the flexibility of production in relation to the labour factor was significantly higher in the group of farms managed by farmers with higher-level education in two out of four analysed macro-regions and on a national scale. In addition, human capital approximated by the level of education had a positive effect on the average and marginal productivity of the analysed farms

Natural and Anthropogenic Changes in the Environment in the Middle Ondava Basin (Eastern Slovakia) during the Neolithic Period

The paper summarizes the geomorphological results of a research project focused on palaeogeographical and archaeological characteristics of a Neolithic settlement in the middle Ondava Basin (north-west part of the Eastern Slovakian Lowland). Investigations on an Early Neolithic (ca. 5500-5100 BC) settlement in Moravany were carried out as part of the project. Palaeogeographical studies were carried out in the neighbouring territory of this site. The Holocene alluvia detected there were much younger than the Neolithic and no distinct traces of the activity of Neolithic people were recorded. Extremely important data were obtained in Kladzany. The general structure of the river valley records the erosional phase of the end of the Pleistocene. In the Early Holocene, the Ondava river cut off the upper part of the palaeochannel fill during lateral migration. A slow process of aggradation was noted during the Neolithic since soil-forming "kept up" with the sedimentation. A change in the rhythm of the overbank deposition occurred after 5,830±40 BP which led to the fossilization of the soil by an over 1 m thick layer of silts. It is difficult to determine whether it is related to human activity