Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces
Yazarlar (2)
Sevinc Z. Khaligova
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA (Q2) | ||
| Dergi ISSN | 1224-1784 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2013 |
| Cilt / Sayı / Sayfa | 21 / 2 / 111–130 | DOI | 10.2478/auom-2013-0026 |
| Makale Linki | https://sciendo.com/pdf/10.2478/auom-2013-0026 | ||
| Özet |
| We prove that the anisotropic fractional maximal operator M-alpha,M-sigma and the anisotropic Riesz potential operator I alpha,sigma , 0 < alpha < vertical bar sigma vertical bar are bounded from the anisotropic modified Morrey space (L) over tilde (1,b,sigma)(R-n) to the weak anisotropic modified Morrey space W (L) over tilde (q,b,sigma)(R-n) if and only if alpha/vertical bar sigma vertical bar <= 1-1-/q <= alpha/(vertical bar sigma vertical bar(1-b)) and from (L) over tilde (p,b,sigma)(R-n) to (L) over tilde (q,b,sigma)(R-n) if and only if, alpha/vertical bar sigma vertical bar <= 1/p - 1/q <= alpha/(1-b)vertical bar sigma vertical bar). In the limiting case vertical bar sigma vertical bar (1-b)/alpha <= p <= vertical bar sigma vertical bar/alpha we prove that the operator M-alpha,M-sigma is bounded from (L) over tilde (p,b,sigma)(R-n) to L-infinity(R-n) and the modified anisotropic Riesz potential operator (I) over tilde (alpha,sigma) is bounded from (L) over tilde (p,b,sigma)(R-n) to BMO sigma (R-n). |
| Anahtar Kelimeler |
| anisotropic Riesz potential | anisotropic fractional maximal function | anisotropic modified Morrey space | anisotropic BMO space |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları |