On grand Sobolev spaces and pointwise description of Banach function spaces

Jain, Pankaj; Molchanova, Anastasia; Singh, Monika; Vodop’yanov, S. K.

doi:10.1016/j.na.2020.112100

Cited by 9 publications

(4 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…holds for some constant C and almost all x, y ∈ Ω with B(x, 3|x − y|) ⊂ Ω. This result has been recently obtained in [14] by P. Jain, A. Molchanova, M. Singh, and S. Vodopyanov for the real-valued case. It is easy to see that the proof of [14, Theorem 2.2] works for vector-valued functions as well.…”

Section: A Maximal Function Characterizationsupporting

confidence: 63%

Vector-valued Sobolev spaces based on Banach function spaces

Evseev¹

2020

Preprint

View full text Add to dashboard Cite

It is known that for Banach valued functions there are several approaches to define a Sobolev class. We compare the usual definition via weak derivatives with the Reshetnyak-Sobolev space and with the Newtonian space; in particular, we provide sufficient conditions when all three agree. As well we revise the difference quotient criterion and the property of Lipschitz mapping to preserve Sobolev space when it acting as a superposition operator.

show abstract

Section: A Maximal Function Characterizationsupporting

confidence: 63%

Vector-valued Sobolev spaces based on Banach function spaces

Evseev¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…We refer to [15] and the references therein. For some very recent updates on grand Lebesgue spaces, we mention [8], [11], [14], [17], [18], [19], [23].…”

Section: Extrapolation Results In Grand Lebesgue Spacesmentioning

confidence: 99%

Rubio de Francia Extrapolation Theorems for Quasi-Monotone Functions

Singh¹,

Panchal²,

Jain³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The conclusion is that W 1,p (Ω) is not a Banach lattice (for a delicate result in this direction see Pełczyński, Wojciechowski [131]). We stress, however, that there are situations where the lattice norm property is not needed for the whole Sobolev space, but just for the space to which f and |Df | belong (see the recent study in Jain, Molchanova, Singh, Vodopyanov [74], where a characterization in terms of the boundedness of the maximal operator is proved). We recall here also another example, which is in a finite dimensional vector space.…”

Section: Banach Latticementioning

confidence: 99%