A new class of function spaces connecting Triebel–Lizorkin spaces and Q spaces

By Dachun Yang, Wen Yuan. 2008

185 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc3e214034a2cd4c3adc40a122ea823d15722ec4

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Citations in the corpus

Generalized Morrey spaces and trace operator (2016, background): “Yang and Yuan investigated Besov type spaces and Triebel-Lizorkin type spaces in [85, 86].”
Relations among Besov-type spaces, Triebel–Lizorkin-type spaces and generalized Carleson measure spaces (2011, methodology): “question, motivated by the Carleson measure characterization of Qα(R) spaces in [1], we in [15] introduced the Triebel-Lizorkin-type spaces Ḟ s,τ p,q (Rn) with s ∈ R, τ ∈ [0,∞), p ∈ (1,∞) and q ∈ (1,∞] and their preduals, the Triebel-Lizorkin-Hausdorff spaces FḢ p,q (Rn) with s ∈ R, p ∈ (1,∞), q ∈ [”
New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets (2011, background): “1) Recall that the homogeneous Besov-type space Ḃ p,q (Rn) and Triebel-Lizorkin-type space Ḟ s,τ p,q (Rn) are defined as follows; see [57, 58].”
Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, background): “Recently, to clarify the relations among Besov spaces, Triebel-Lizorkin spaces and Q spaces (see [16, 24]), Besov-type spaces B p,q (R ) and Triebel-Lizorkin-type spaces F s,τ p,q (R ) and their homogeneous counterparts for all admissible parameters were introduced and studied in [76, 77, 80].”
Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “On the other hand, Besov-type spaces B p,q (R ) and Triebel-Lizorkin spaces F s,τ p,q (R ) and their homogeneous counterparts for all admissible parameters were introduced in [68, 69, 78] in order to clarify the relations among Besov spaces, Triebel-Lizorkin spaces and Q space (see [12, 19]).”
Interpolation of Morrey-Campanato and related smoothness spaces (2014, background): “In the last two decades, partly due to the study of Navier-Stokes equations, there is an increasing interest in the construction of smoothness spaces based on Morrey spaces (in what follows called Morrey-type spaces); see, for example, [34, 40, 49, 79, 86, 91, 92, 97].”
New Besov-type spaces and Triebel–Lizorkin-type spaces including Q spaces (2010, methodology): “Remark 6.1 (i) If p = q ,t henB ˙ H s ,τ q, q (R n ) = F ˙ H s ,τ q q, q (R n ) ,w hereF ˙ H s ,τ p, q (R n ) were introduced in [ 35, Section 5 ].”
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].”