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- W4365451208 abstract "We give Littlewood–Paley type characterizations for Besov–Triebel–Lizorkin–type spaces $$mathscr {B}_{pq}^{stau },mathscr {F}_{pq}^{stau }$$ and Besov-Morrey spaces $$mathcal N_{uqp}^s$$ on a special Lipschitz domain $$Omega subset mathbb R^n$$ : for a suitable sequence of Schwartz functions $$(phi _j)_{j=0}^infty $$ , $$begin{aligned} Vert fVert _{mathscr {B}_{pq}^{stau }(Omega )}&textstyle approx sup _{Ptext { dyadic cubes}}|P|^{-tau }Vert (2^{js}phi _j*f)_{j=log _2ell (P)}^infty Vert _{ell ^q(L^p(Omega cap P))}; Vert fVert _{mathscr {F}_{pq}^{stau }(Omega )}&textstyle approx sup _{Ptext { dyadic cubes}}|P|^{-tau }Vert (2^{js}phi _j*f)_{j=log _2ell (P)}^infty Vert _{L^p(Omega cap P;ell ^q)}; Vert fVert _{mathcal N_{uqp}^{s}(Omega )}&textstyle approx big Vert big (sup _{Ptext { dyadic cubes}}|P|^{frac{1}{u}-frac{1}{p}}cdot 2^{js}Vert phi _j*fVert _{L^p(Omega cap P)}big )_{j=0}^infty big Vert _{ell ^q}. end{aligned}$$ We also show that $$Vert fVert _{mathscr {B}_{pq}^{stau }(Omega )}$$ , $$Vert fVert _{mathscr {F}_{pq}^{stau }(Omega )}$$ and $$Vert fVert _{mathcal N_{uqp}^{s}(Omega )}$$ have equivalent (quasi-)norms via derivatives: for $$mathscr {X}^bullet in {mathscr {B}_{pq}^{bullet ,tau },mathscr {F}_{pq}^{bullet ,tau },mathcal N_{uqp}^bullet }$$ , we have $$Vert fVert _{mathscr {X}^s(Omega )}approx sum _{|alpha |le m}Vert partial ^alpha fVert _{mathscr {X}^{s-m}(Omega )}$$ . In particular $$Vert fVert _{mathscr {F}_{infty q}^s(Omega )}approx sum _{|alpha |le m}Vert partial ^alpha fVert _{mathscr {F}_{infty q}^{s-m}(Omega )}approx sup _{P}|P|^{-n/q}Vert (2^{js}phi _j*f)_{j=log _2ell (P)}^infty Vert _{ell ^q(L^q(Omega cap P))}$$ ." @default.
- W4365451208 created "2023-04-15" @default.
- W4365451208 creator A5002711296 @default.
- W4365451208 date "2023-04-01" @default.
- W4365451208 modified "2023-10-13" @default.
- W4365451208 title "Some Intrinsic Characterizations of Besov–Triebel–Lizorkin–Morrey–Type Spaces on Lipschitz Domains" @default.
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- W4365451208 doi "https://doi.org/10.1007/s00041-023-10001-x" @default.
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