| 1. |
- Astashkin, Sergey, et al.
(författare)
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Isomorphic structure of Cesàro and Tandori spaces
- 2019
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Ingår i: Canadian Journal of Mathematics - Journal Canadien de Mathematiques. - : Cambridge University Press. - 0008-414X .- 1496-4279. ; 71:3, s. 501-532
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the isomorphic structure of the Cesàro spaces and their duals, the Tandori spaces. The main result states that the Cesàro function space Ces∞ and its sequence counterpart ces∞ are isomorphic. This is rather surprising since Ces∞ (like Talagrand’s example) has no natural lattice predual. We prove that ces∞ is not isomorphic to ℓ∞ nor is Ces∞ isomorphic to the Tandori space L1 with the norm ∥f∥L1 = ∥f∥L1, where f(t) = esssups≥tf(s). Our investigation also involves an examination of the Schur and Dunford–Pettis properties of Cesàro and Tandori spaces. In particular, using results of Bourgain we show that a wide class of Cesàro–Marcinkiewicz and Cesàro–Lorentz spaces have the latter property.
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| 2. |
- Astashkin, Sergey V., et al.
(författare)
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Lp + L∞ and Lp n L∞ are not Isomorphic for all 1 ≤ p < ∞, p ≠ 2
- 2018
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Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 146:5, s. 2181-2194
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Tidskriftsartikel (refereegranskat)abstract
- We prove the result stated in the title. It comes as a consequence of the fact that the space Lp n L∞, 1 = p < ∞, p ≠ 2, does not contain a complemented subspace isomorphic to Lp. In particular, as a subproduct, we show that Lp nL∞ contains a complemented subspace isomorphic to l2 if and only if p = 2.
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| 3. |
- Astashkin, Sergey V., et al.
(författare)
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Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
- 2018
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Ingår i: Comptes rendus. Mathematique. - : Elsevier. - 1631-073X .- 1778-3569. ; 356:6, s. 661-665
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Tidskriftsartikel (refereegranskat)abstract
- We prove that if 1≤p,q≤∞1≤p,q≤∞, then the spaces Lp+LqLp+Lq and Lp∩LqLp∩Lq are isomorphic if and only if p=qp=q. In particular, L2+L∞L2+L∞ and L2∩L∞L2∩L∞ are not isomorphic, which is an answer to a question formulated in [2].
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| 4. |
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| 5. |
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| 6. |
- Berezhnoǐ, Eugenii I., et al.
(författare)
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Represensibility of cones of monotone functions in weighted Lebesgue spaces and extrapolation of operators on these cones
- 2018
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Ingår i: St. Petersburg Mathematical Journal. - : American Mathematical Society (AMS). - 1061-0022 .- 1547-7371. ; 29:4, s. 545-574
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that a sublinear operator is bounded on the cone of monotone functions if and only if a certain new operator related to the one mentioned above is bounded on a certain ideal space defined constructively. This construction is used to provide new extrapolation theorems for operators on the cone in weighted Lebesgue spaces.
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| 7. |
- Burtseva, Evgeniya, 1988-, et al.
(författare)
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Boundedness of the Riesz potential in central Morrey-Orlicz spaces
- 2022
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Ingår i: Positivity (Dordrecht). - : Springer Nature. - 1385-1292 .- 1572-9281. ; 26:1
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Tidskriftsartikel (refereegranskat)abstract
- Boundedness of the maximal operator and the Calderón–Zygmund singular integral operators in central Morrey–Orlicz spaces were proved in papers (Maligranda et al. in Colloq Math 138:165–181, 2015; Maligranda et al. in Tohoku Math J 72:235–259, 2020) by the second and third authors. The weak-type estimates have also been proven. Here we show boundedness of the Riesz potential in central Morrey–Orlicz spaces and the corresponding weak-type version.
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| 8. |
- Ciesielska, Danuta, et al.
(författare)
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Alfred Rosenblatt (1880-1947). Polish-Peruvian mathematician
- 2019
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Ingår i: Banach Center Publications. - Warszawa : Polish Academy of Sciences. - 0137-6934 .- 1730-6299. ; 119, s. 57-108
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Tidskriftsartikel (refereegranskat)abstract
- Alfred Rosenblatt (1880-1947) was a Polish mathematician born into a Jewish family in Krakow (Kraków, Poland). He studied in Vienna, Krakow, Göttingen, and worked at the Jagiellonian University in Krakow (1910-1936) and at the University of San Marcos in Lima, Peru (1936-1947). During the Second World War, Rosenblatt accepted Peruvian citizenship. His work was important for the development of mathematics in Peru, including the foundation of the National Academy of Exact Sciences, Physics and Natural Sciences in Lima. He is mentioned among the four mathematicians of the twentieth century most important for Peru (F. Villarreal, G. Garcia Diaz, A. Rosenblatt and J. Tola Pasquel). He spent the first half of 1947 on a scholarship at the Institute for Advanced Study in Princeton and had several lectures at other universities in the USA.Rosenblatt published almost three hundred scientific papers in various fields of pure and applied mathematics, including ordinary and partial differential equations, algebraic geometry, theory of analytic functions, probability, mathematical physics, three-body problem, hydrodynamics and other applications of mathematics. About 180 papers were published in the years of his work in Poland and about 120 in the years he worked in Peru. His publications are in Polish, German, French, Italian, Spanish and English. Rosenblatt participated actively in four International Congresses of Mathematicians: Cambridge (1912), Strasbourg (1920), Bologna (1928), Zurich (1932). He presented three talks in Bologna and one in Zurich.We describe Alfred Rosenblatt's life and important parts of his work in detail. We have made an effort to see all his papers, so as not to miss any of his achievements in mathematics and applications, including papers and information written in Spanish; e.g., [Ro11], [Ro13]-[Ro16] and [Ro20]. We have already written three articles, two in Polish [Ro8], [Ro9] and one in Russian [Ro12], to introduce him to Polish and Russian mathematicians. Now we want to do the same for a wider range of scientists with this article in English. Some information on Rosenblatt can also be found in [Ro1]-[Ro6], [Ro10] and [Ro17]-[Ro19].
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| 9. |
- Ciesielska, Danuta, et al.
(författare)
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Doktoraty Polaków w Getyndze. Matematyka
- 2019
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Ingår i: Analecta. Studia i materiały z dziejów nauki. - Warszawa : Instytut Historii Nauki PAN. - 1509-0957. ; 28:2, s. 73-116
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Tidskriftsartikel (refereegranskat)abstract
- The article provides information about the documents held in the archives of the Georg August University in Göttingen (Georg-August-Universität Göttingen), pertaining to the efforts of Poles who wanted to obtain a doctorate in mathematics. In the years 1892–1922, ten Poles were awarded doctorates in exact sciences in Göttingen, including fi ve in mathematics. Michał Feldblum from Warsaw, Hugo Steinhaus from Jasło and Arnold Walfi sz from Warsaw received doctorates in pure mathematics, Władysław Bortkiewicz from Saint Petersburg in mathematical statistics and Jan Kroo from Krakow in mathematical physics. From the documents related to these fi ve doctoral proceedings, the authors have extracted the information that has not been hitherto published, including the opinions on doctoral dissertations (by Hilbert, Landau, Lexis, and Voigt), exam questions, opinions on the results achieved by doctoral students, and handwritten CVs. The documents have been translated into Polish.
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| 10. |
- Jóźwik, Izabela, et al.
(författare)
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Stefan Kempisty (1892-1940)
- 2017
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Ingår i: Antiquitates Mathematicae. - : Polskie Towarzystwo Matematyczne. - 1898-5203 .- 2353-8813. ; 11:1, s. 61-111
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Tidskriftsartikel (refereegranskat)abstract
- Stefan Kempisty był polskim matematykiem zajmujacym sie funkcjami zmiennej rzeczywistej, teoria mnogosci, całkami, funkcjami przedziału i teoria pola powierzchni. W 1919 roku obronił prace doktorska ,,O funkcjach nawpołciagłych" na Uniwersytecie Jagiellonskim w Krakowie, a promotorem był Kazimierz Zorawski. W grudniu 1924 roku habilitował sie na Uniwersytecie Warszawskim i w latach 1920--1939 pracował na Uniwersytecie Stefana Batorego w Wilnie. Opublikował ponad czterdziesci prac naukowych i trzy podreczniki z analizy rzeczywistej oraz jedna monografie. Reprezentował w swoich pracach i na seminariach szkołe warszawska. Nazwisko Kempistego w matematyce pojawia sie w zwiazku z definicja funkcji quasi-ciagłej, roznymi ciagłosciami funkcji wielu zmiennych, klasyfikacja funkcji Baire'a, Younga i Sierpinskiego, funkcjami przedziału oraz całkami Denjoy'a i Burkilla.Zainteresowalismy sie Kempistym ze wzgledu na jego dorobek naukowy, pewne niewyjasnione informacje osobiste oraz 125 rocznice urodzin przypadajaca w 2017 roku. Przedstawiamy wiec jego biografie, udział w konferencjach, sylwetki zony Eugenii i corki Marii oraz jego dorobek naukowy. Wszystkie informacje o nim pochodza z wielu zrodeł.
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