PDF полного текста (443 kB) Список цитирования (2)

Аннотация: In this paper embedding relations between weighted complementary local Morrey-type spaces $^cLM_{p\theta,\omega}(\mathbb{R}^n,v)$ and weighted local Morrey-type spaces $LM_{p\theta,\omega}(\mathbb{R}^n,v)$ are characterized. In particular, two-sided estimates of the optimal constant $c$ in the inequality
$$
\left( \int_0^\infty\left( \int_{B(0,t)} f(x)^{p_2}v_2(x)\,dx \right)^{\frac{q_2}{p_2}}u_2(t)\,dt \right)^{\frac1{q_2}} \leqslant c \left(\int_0^\infty\left(\int_{^cB(0,t)}f(x)^{p_1}v_1(x)\,dx\right)^{\frac{q_1}{p_1}}u_1(t)\,dt\right)^{\frac1{q_1}},\quad f\geqslant0
$$
are obtained, where $p_1$, $p_2$, $q_1$, $q_2\in(0,\infty)$, $p_2\leqslant q_2$ and $u_1$, $u_2$ and $v_1$, $v_2$ are weights on $(0,\infty)$ and $\mathbb{R}^n$, respectively. The proof is based on the combination of the duality techniques with estimates of optimal constants of the embedding relations between weighted local Morrey-type and complementary local Morrey-type spaces and weighted Lebesgue spaces, which allows to reduce the problem to using of the known Hardy-type inequalities.

Ключевые слова и фразы: local Morrey-type spaces, embeddings, iterated Hardy inequalities.

Финансовая поддержка	Номер гранта
Grantová Agentura České Republiky	P201-13-14743S RVO 67985840
Национальный научный фонд имени Шота Руставели	DI/9/5-100/13
The research of A. Gogatishvili was partially supported by the grant P201-13-14743S of the Grant Agency of the Czech Republic and RVO: 67985840 and by Shota Rustaveli National Science Foundation, grant no. DI/9/5-100/13 (Function spaces, weighted inequalities for integral operators and problems of summability of Fourier series).

Поступила в редакцию: 06.12.2016

Реферативные базы данных:

Образец цитирования: A. Gogatishvili, R. Mustafayev, T. Ünver, “Embedding relations between weighted complementary local Morrey-type spaces and weighted local Morrey-type spaces”, Eurasian Math. J., 8:1 (2017), 34–49

Цитирование в формате AMSBIB

Образцы ссылок на эту страницу:

https://www.mathnet.ru/rus/emj246

https://www.mathnet.ru/rus/emj/v8/i1/p34

Эта публикация цитируется в следующих статьяx:

1. Sh. Nakamura, Y. Sawano, H. Tanaka, “Weighted local Morrey spaces”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 45 (2020), 67–93          
2. R. Mustafayev, A. Kucukaslan, “An extension of the Muckenhoupt-Wheeden theorem to generalized weighted Morrey spaces”, Georgian Math. J., 28:4 (2021), 595–610          

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles