A note on L(\infty, q) spaces and Sobolev embeddings

Bastero, Jesús; Milman, Mario; Blasco, Francisco

doi:10.1512/iumj.2003.52.2364

Cited by 56 publications

(104 citation statements)

References 14 publications

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“…It is known that by [17], [1,3], L(∞, q) are defined as the class of all measurable functions f for which f * (t) < ∞ for all t > 0 and for which f * * (t) − f * (t) is a bounded function of t such that…”

Section: T X M W F (T) = E 2πiw(t−x) F (T − X) or M W T X F (T) = E 2mentioning

confidence: 99%

On Lorentz mixed normed modulation spaces

Sandıkçı

2012

J. Pseudo-Differ. Oper. Appl.

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This paper is a study on a new kind modulation spaces M(P, Q) (R d ) and A(P, Q, r )(R d ) for indices in the range 1 < P < ∞, 1 ≤ Q < ∞ and 1 ≤ r < ∞, modelled on Lorentz mixed norm spaces instead of mixed norm L P spaces as the spaces 2006). First, we prove the main properties of these spaces. Later, we describe the dual spaces and determine the multiplier spaces for both of them. Moreover, we investigate the boundedness of Weyl operators and localization operators on M(P, Q)(R d ). Finally, we give an interpolation theorem for M(P, Q)(R d ).Keywords Gabor transform · Lorentz mixed norm space · modulation space · Weyl operator · Multiplier IntroductionIn this paper we will work on R d with Lebesgue measure dx. We denote by C c (R d ) and S(R d ) the spaces of complex-valued continuous functions with compact support and the space of complex-valued continuous functions on R d rapidly decreasing at infinity, respectively. Let f be a complex valued measurable function on R d . The operators T x f (t) = f (t − x) and M w f (t) = e 2πiwt f (t) are called translation and A. Sandıkçı (B)

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Section: T X M W F (T) = E 2πiw(t−x) F (T − X) or M W T X F (T) = E 2mentioning

confidence: 99%

On Lorentz mixed normed modulation spaces

Sandıkçı

2012

J. Pseudo-Differ. Oper. Appl.

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“…Moreover, in the limiting case q = p p−1 , then s = ∞ and we 1 The restriction on the Boyd indices is only required to guarantee that the inequality g * * X ≤ c X g X , holds for all g ∈ X.…”

Section: Introductionmentioning

confidence: 99%

Self Improving Sobolev-Poincaré Inequalities, Truncation and Symmetrization

Martín

Milman

2008

Potential Anal

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“…The latter two spaces are of special interest in interpolation theory. The space L(∞, q) of [2] is yet another example, related to the two preceding ones. Before formulating and proving our main result it is convenient to present a lemma which will be needed later.…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 98%