FRANKE-JAWERTH EMBEDDINGS FOR BESOV AND TRIEBEL-LIZORKIN SPACES WITH VARIABLE EXPONENTS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390880" target="_blank" >RIV/00216208:11320/18:10390880 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.5186/aasfm.2018.4310" target="_blank" >https://doi.org/10.5186/aasfm.2018.4310</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5186/aasfm.2018.4310" target="_blank" >10.5186/aasfm.2018.4310</a>

Jazyk výsledku

angličtina

Název v původním jazyce

FRANKE-JAWERTH EMBEDDINGS FOR BESOV AND TRIEBEL-LIZORKIN SPACES WITH VARIABLE EXPONENTS

Popis výsledku v původním jazyce

The classical Jawerth and Franke embeddings F-p0,q(s0)(R-n) hooked right arrow B-p1,p0(s1)(R-n) and B-p0,p1(s0)(R-n) hooked right arrow F-p1,q1(s1)(R-n) are versions of Sobolev embedding between the scales of Besov and Triebel-Lizorkin function spaces for s(0) &gt; s(1) and s(0) - n/p(0) = s(1) - n/p(1). We prove Jawerth and Franke embeddings for the scales of Besov and Triebel-Lizorkin spaces with all exponents variable F-p0(.),q(.)(s0(.))(R-n) hooked right arrow B-p1(.),p0(.)(s1(.))(R-n) and B-p0(.),q(.)(s0(.))(R-n) hooked right arrow F-p1(.),p0(.)(s1(.))(R-n), respectively, if inf(x is an element of Rn)(s(0)(x) - s(1)(x)) &gt; 0 and s(0)(x) = n/P-0(x) = s(1)(x) - n/p(1)(x), x is an element of R-n. We work exclusively with the associated sequence spaces b(P(.),q(.))(s(.))(R-n) and f(P(.),q(.))(s(.))(R-n), which is justified by well known decomposition techniques. We give also a different proof of the Franke embedding in the constant exponent case which avoids duality arguments and interpolation. Our results hold also for 2-microlocal function spaces B-P(.),q(.)(omega)(R-n) and F-P(.),q(.)(omega)(R-n) which unify the smoothness scales of spaces of variable smoothness and generalized smoothness spaces.

Název v anglickém jazyce

FRANKE-JAWERTH EMBEDDINGS FOR BESOV AND TRIEBEL-LIZORKIN SPACES WITH VARIABLE EXPONENTS

Popis výsledku anglicky

The classical Jawerth and Franke embeddings F-p0,q(s0)(R-n) hooked right arrow B-p1,p0(s1)(R-n) and B-p0,p1(s0)(R-n) hooked right arrow F-p1,q1(s1)(R-n) are versions of Sobolev embedding between the scales of Besov and Triebel-Lizorkin function spaces for s(0) &gt; s(1) and s(0) - n/p(0) = s(1) - n/p(1). We prove Jawerth and Franke embeddings for the scales of Besov and Triebel-Lizorkin spaces with all exponents variable F-p0(.),q(.)(s0(.))(R-n) hooked right arrow B-p1(.),p0(.)(s1(.))(R-n) and B-p0(.),q(.)(s0(.))(R-n) hooked right arrow F-p1(.),p0(.)(s1(.))(R-n), respectively, if inf(x is an element of Rn)(s(0)(x) - s(1)(x)) &gt; 0 and s(0)(x) = n/P-0(x) = s(1)(x) - n/p(1)(x), x is an element of R-n. We work exclusively with the associated sequence spaces b(P(.),q(.))(s(.))(R-n) and f(P(.),q(.))(s(.))(R-n), which is justified by well known decomposition techniques. We give also a different proof of the Franke embedding in the constant exponent case which avoids duality arguments and interpolation. Our results hold also for 2-microlocal function spaces B-P(.),q(.)(omega)(R-n) and F-P(.),q(.)(omega)(R-n) which unify the smoothness scales of spaces of variable smoothness and generalized smoothness spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annales Academiae Scientiarum Fennicae - Mathematica

ISSN

1239-629X

e-ISSN

—

Svazek periodika

43

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

FI - Finská republika

Počet stran výsledku

23

Strana od-do

187-209

Kód UT WoS článku

000429434500009

EID výsledku v databázi Scopus

2-s2.0-85042879987