A new framework for generalized Besov-type and Triebel–Lizorkin-type spaces

Liang, Yiyu; Yang, Dachun; Yuan, Wen; Sawano, Yoshihiro; Ullrich, Tino

doi:10.4064/dm489-0-1

Cited by 79 publications

(100 citation statements)

References 76 publications

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“…Regular coverings and related atomic decompositions, also restricted to τ = 0, have been discussed in [33]; see also [38]. Atomic decompositions of Besov-type spaces have been investigated in [53] and [23]. Our proof of Theorem 2.15 is more or less parallel to those given in the quoted papers.…”

Section: Radial Subspacesmentioning

confidence: 82%

The radial lemma of Strauss in the context of Morrey spaces

Sickel¹,

Yang²,

Yuan³

2014

Ann. Acad. Sci. Fenn. Math.

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Section: Radial Subspacesmentioning

confidence: 82%

The radial lemma of Strauss in the context of Morrey spaces

Sickel¹,

Yang²,

Yuan³

2014

Ann. Acad. Sci. Fenn. Math.

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“…We remark that

L_{p (\cdot)}^{ϕ} (ℓ_{q (\cdot)})

is a quasi‐normed space that coincides with the mixed Lebesgue‐sequence space

L_{p (\cdot)} (ℓ_{q (\cdot)})

when

ϕ \equiv 1

. The case of

q (\cdot) = q

constant and

ϕ false(Q false) : = {| Q |}^{τ}

for all cubes Q and

τ \in [0, \infty)

, has also been considered in .…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…Moreover, also the spaces

F_{\infty, q}^{s} false(R^{n} false)

and the Triebel–Lizorkin–Morrey spaces

{scriptE}_{u, p, q}^{s} false(R^{n} false)

are included, as

F_{\infty, q}^{s} false(R^{n} false) = F_{p, q}^{s, 1 / p} false(R^{n} false)

for

p \in (0, \infty)

, and

{scriptE}_{u, p, q}^{s} false(R^{n} false) = F_{p, q}^{s, 1 / p - 1 / u} false(R^{n} false)

0 < p \leq u < \infty

, cf. . (iv)When q , s are constant exponents and

ϕ false(Q false) : = {| Q |}^{τ}

for all cubes Q and

τ \in [0, \infty)

, then

F_{p (\cdot), q (\cdot)}^{s false(\cdot false), ϕ} false(R^{n} false) = F_{p (\cdot), q}^{s, τ} false(R^{n} false)

which was investigated in . (v)The condition

p^{+} < \infty

, included in

p \in P ({double-struckR}^{n})

, is quite natural since it also exists in the case ...…”

Section: Notation and Definitionsmentioning

confidence: 99%

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Characterization of Triebel–Lizorkin type spaces with variable exponents via maximal functions, local means and non‐smooth atomic decompositions

Gonçalves

Moura

2018

Mathematische Nachrichten

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In this paper we study the maximal function and local means characterizations and the non‐smooth atomic decomposition of the Triebel–Lizorkin type spaces with variable exponents Fp(·),q(·)sfalse(·false),ϕfalse(Rnfalse). These spaces were recently introduced by Yang et al. and cover the Triebel–Lizorkin spaces with variable exponents Fp(·),q(·)s(·)false(Rnfalse) as well as the classical Triebel–Lizorkin spaces Fp,qsfalse(Rnfalse), even the case when p=∞. Moreover, covered by this scale are also the Triebel–Lizorkin‐type spaces Fp,qs,τfalse(Rnfalse) with constant exponents which, in turn cover the Triebel–Lizorkin–Morrey spaces. As an application we obtain a pointwise multiplier assertion for those spaces.

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“…Another type of generalization of the Triebel-Lizorkin spaces by using the Peetre's maximal function is introduced in [26]. The main theme of this section is to study the Triebel-Lizorkin spaces associated with r.i.q.B.f.s.…”

Section: Triebel-lizorkin Spaces and Hardy Spacesmentioning

confidence: 99%

Fourier integrals and Sobolev embedding on rearrangement invariant quasi-Banach function spaces

Ho¹

2016

Ann. Acad. Sci. Fenn. Math.

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Abstract. We extend the mapping properties for the fractional integral operators, the convolution operators, the Fourier integral operators and the oscillatory integral operators to rearrangementinvariant quasi-Banach function spaces. We also generalize the Fourier restriction theorem and the Sobolev embedding theorem to rearrangement-invariant quasi-Banach function spaces. We obtain the above results by introducing two families of rearrangement-invariant quasi-Banach function spaces. Furthermore, these two families of rearrangement-invariant quasi-Banach function spaces also give us some embedding and interpolation results of Triebel-Lizorkin type spaces and Hardy type spaces built on rearrangement-invariant quasi-Banach function spaces.

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A new framework for generalized Besov-type and Triebel–Lizorkin-type spaces

Cited by 79 publications

References 76 publications

The radial lemma of Strauss in the context of Morrey spaces

The radial lemma of Strauss in the context of Morrey spaces

Characterization of Triebel–Lizorkin type spaces with variable exponents via maximal functions, local means and non‐smooth atomic decompositions

Fourier integrals and Sobolev embedding on rearrangement invariant quasi-Banach function spaces

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