Maximal Function Methods for Sobolev Spaces

Kinnunen, Juha; Lehrbäck, Juha; Vähäkangas, Antti V.

doi:10.1090/surv/257

Cited by 11 publications

(3 citation statements)

References 319 publications

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“…which is a well known classical result (see the recent monograph [24]), being the boundedness false when p " 1, 1 ˚" n n´1 " n 1 . I 1 is the Riesz potential operator of order α " 1 given by the expression…”

Section: Some Preliminaries and Their Historymentioning

confidence: 87%

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A tribute to Pola Harboure: Isoperimetric inequalities and the HMS extrapolation theorem

Pérez,

Rela

2023

Revista De La Unión Matemática Argentina

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We give a simpler proof of the Gagliardo estimate with a measure obtained by Franchi, Pérez, and Wheeden [Proc. London Math. Soc. (3) 80 no. 3 (2000), 665-689], and improved by Pérez and Rela [Trans. Amer. Math. Soc. 372 no. 9 (2019), 6087-6133]. This result will be further improved using fractional Poincaré type inequalities with the extra bonus of Bourgain-Brezis-Mironescu as done by Hurri-Syrjänen, Martínez-Perales, Pérez, and Vähäkangas [Internat. Math. Res. Notices (2022), rnac246] with a new argument. This will be used with the HMS extrapolation theorem to get L p type result.

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Section: Some Preliminaries and Their Historymentioning

confidence: 87%

“…when 1 ď p ă n. Extensions and new variations of this estimate can be found in [6,7]. The most common approach to prove (2.1) is based on the following pointwise estimate which controls the oscillation of the function by the fractional integral (see [24,34])…”

Section: Some Preliminaries and Their Historymentioning

confidence: 99%

A tribute to Pola Harboure: Isoperimetric inequalities and the HMS extrapolation theorem

Pérez,

Rela

2023

Revista De La Unión Matemática Argentina

View full text Add to dashboard Cite

show abstract

“…Harnack inequalities for double phase problems were obtained by Di Benedetto-Trudinger [11], Baroni-Colombo-Mingione [1] and the references therein. See also Kinnunen-Lehrbäck-Vähäkangas [26], Marcellini [33,34] and Mingione-Rǎdulescu [39] for other results and literature reviews.…”

Section: Introductionmentioning

confidence: 99%