Characterization of Function Spaces for the Dunkl Type Operator on the Real Line

Kallel, Samir

doi:10.1007/s11118-013-9366-5

Cited by 8 publications

(10 citation statements)

References 16 publications

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“…Before giving a central result of this section, we need to recall the definition of the spaces ∧ k α,p,q (IR) (see [17]) and the following auxiliary lemmas.…”

Section: Dunkl-bessel Potentialsmentioning

confidence: 99%

“…is finite, then according to the Proposition 6.1(v) and Remark (5.14) of [17], it is easy to see that…”

mentioning

confidence: 90%

“…In [17], we have introduced and characterized for α > 0 and 1 ≤ p, q ≤ ∞ the generalized Dunkl-Lipschitz spaces ∧ k α,p,q (IR) associated with the Dunkl operator with parameter k ≥ 0…”

Section: Introductionmentioning

confidence: 99%

“…His method leaned on a theory of Riesz potentials for temperatures. Additionally, for α > 0, the generalized DunklLipschitz spaces or Besov-Dunkl spaces have been studied extensively by several mathematicians and characterized in different ways by many authors (see [1,2,3,8,17,18,19]). …”

Section: Introductionmentioning

confidence: 99%

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Generalized Dunkl-Lipschitz spaces

Kallel¹

2016

J. Pseudo-Differ. Oper. Appl.

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“…Before giving a central result of this section, we need to recall the definition of the spaces ∧ k α,p,q (IR) (see [17]) and the following auxiliary lemmas.…”

Section: Dunkl-bessel Potentialsmentioning

confidence: 99%

“…is finite, then according to the Proposition 6.1(v) and Remark (5.14) of [17], it is easy to see that…”

mentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Dunkl-Lipschitz spaces

Kallel¹

2016

J. Pseudo-Differ. Oper. Appl.

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“…In , we have introduced and characterized the generalized Dunkl–Lipschitz spaces

\land_{α, p, q}^{k} false(I R false)

, when

α \in I R

and

1 \leq p, q \leq \infty

. Also, for any α,

β \in I R

, the Dunkl–Bessel potential

J_{β}^{k}

is proved to be a topological isomorphism from

\land_{α, p, q}^{k} false(I R false)

onto

\land_{α + β, p, q}^{k} false(I R false)

.…”

Section: Introductionmentioning

confidence: 99%

Some results on generalized Dunkl–Lipschitz spaces

Kallel

2019

Mathematische Nachrichten

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In this paper we study certain relations between the Dunkl-Sobolev classes of fractional order  , ( ) and the generalized Dunkl-Lipschitz classes ∧ , , ( ). Next, we show a Dunkl-Hardy-Littlewood theorem for -temperatures and its dual. Also, we give some theorems on Dunkl convolutions of Dunkl-Lipschitz functions. Finally, we establish some results concerning the Dunkl transforms of functions and distributions belonging to generalized Dunkl-Lipschitz spaces. K E Y W O R D SDunkl operator, Dunkl transform, generalized Dunkl-Lipschitz space, maximal functions M S C ( 2 0 1 0 ) 26A16, 42A38, 42B25, 46E30 www.mn-journal.org

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Lipschitz and Triebel–Lizorkin spaces associated with the Dunkl operators on $$\mathbb {R}^d$$ R d

Kallel

2019

Positivity

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Characterization of Function Spaces for the Dunkl Type Operator on the Real Line

Cited by 8 publications

References 16 publications

Generalized Dunkl-Lipschitz spaces

Generalized Dunkl-Lipschitz spaces

Some results on generalized Dunkl–Lipschitz spaces

Lipschitz and Triebel–Lizorkin spaces associated with the Dunkl operators on $$\mathbb {R}^d$$ R d

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