Besov-Morrey spaces: Function space theory and applications to non-linear PDE

By A. Mazzucato. 2002

245 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6491073e00b711e7e156f865f7036241678f532c

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Citations in the corpus

A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces (2012, unknown): “Another direction is pursued via replacing the space Lp(Rn) by the Morrey space Mu(R); see [48, 52, 53], or generalizations thereof [43, 80, 82, 89, 95, 96, 98, 99, 104].”
Gradient estimates below the duality exponent (2010, background): “See for instance [51] and its references.”
Generalized Morrey spaces and trace operator (2016, background): “She also investigated the pseudo-differential operators as well as the Besov-Morrey spaces on compact oriented Riemannian manifolds [33].”
The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and C1 Domains (2004, methodology): “Other papers dealing with fluid dynamics problems on Riemannian manifolds are [7], [38], [47], [50], [52],”
The Calderón-Zygmund theory for elliptic problems with measure data (2006, background): “ α,q;BR < ∞ if α < 1 kDwkq Lq,θ(A) if α = 1 < ∞ . In any case we let (2.16) kwkWα,q,θ(A) := kwkWα,q(A) +[w]α,q,θ;A . For such spaces and generalizations, see the original papers [15, 16] and [58, 71]. 2.6. Marcinkiewicz spaces. Finally, Marcinkiewicz spaces Mt(A,Rk), t ≥ 1, also called Lore”
About the Regularized Navier–Stokes Equations (2003, unknown): “We skip several details of proofs because they can be found either in [15] or in [20, 25].”
Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces for nondoubling measures (2009, methodology): “In [6, 7, 8, 12] decomposition methods of these function spaces were considered.”
Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces on domains (2010, unknown): “spaces on compact oriented Riemannian manifolds [8].”
Littlewood-Paley spaces (2011, background): “When 0 < p, q < ∞, Bs = l, Bf = L(R) and ω(x, r) = r n pu− n pv , then Ḟ Bs,Bf and its Besov space counterparts are the Triebel-Lizorkin-Morrey spaces and Besov-Morrey spaces; and Morrey type Besov-Triebel spaces in [39, 52] and [53], respectively.”
Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces (2012, methodology): “In [51, 52, 72], a family of function spaces arising from combining the Littlewood–Paley characterization and Morrey spaces is used to study the solutions of some non-linear differential equations, in particular, the Navier–Stokes system in Morrey spaces [29, 40, 51].”
A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces (2009, background): “These function spaces are investigated by changing scales or extending admissible parameters in [3–7].”
Interpolation of Morrey-Campanato and related smoothness spaces (2014, background): “aley assertion in Proposition 5.2(iv) can be found in Mazzucato [59] and Sawano [76]. 5.2 Besov-Morrey and Triebel-Lizorkin-Morrey spaces The following spaces were ﬁrst introduced and investigated in [41,60,78,92]. Deﬁnition 5.4. Let s∈Rand q∈(0,∞]. Let {ϕj}j∈Z+ be the smooth dyadic decomposition of”