About unimprovability the embedding theorems for anisotropic Nikol’skii-Besov spaces with dominated mixed derivates and mixed metric and anisotropic Lorentz spaces
Үстем аралас туындысы және аралас метрикасы бар анизотропты Никольский-Бесов кеңiстiктерi және анизотропты Лоренц кеңiстiктерi үшiн ену теоремаларының жетiлдiрiлмейтiндiгi туралы
О неулучшаемости теорем вложения для анизотропных пространств Никольского-Бесова с доминирующей смешанной производной и смешанной метрикой и анизотропных пространств Лоренца
Toleugazy Y. Kervenev K.Y.
2024E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2024#114Issue 2186 - 196 pp.
The embedding theory of spaces of differentiable functions of many variables studies important connections and relationships between differential (smoothness) and metric properties of functions and has wide application in various branches of pure mathematics and its applications. Earlier, we obtained the embedding theorems of different metrics for Nikol’skii-Besov spaces with a dominant mixed smoothness and mixed metric, and anisotropic Lorentz spaces. In this work, we showed that the conditions for the parameters of spaces in the above theorems are unimprovable. To do this, we built the extreme functions included in the spaces from the left sides of the embeddings and not included in the “slightly narrowed” spaces from the spaces in the right parts of the embeddings.
anisotropic Lorentz spaces , anisotropic Nikol’skii-Besov spaces , embedding theorems , generalized mixed smoothness , mixed metric
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M.V. Lomonosov Moscow State University, Kazakhstan Branch, 11 Kazhymukan street, Astana, 100008, Kazakhstan
Karaganda Buketov University, 28 Universitetskaya street, Karaganda, 100028, Kazakhstan
M.V. Lomonosov Moscow State University
Karaganda Buketov University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026