Singular Integral Operators, Morrey Spaces and Fine Regularity of Solutions to PDE's

Palagachev, Dian K.; Softova, Lubomira G.

doi:10.1023/b:pota.0000010664.71807.f6

Cited by 87 publications

(51 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The classical Morrey spaces were originally introduced by Morrey in [36] to study the local behavior of solutions to second order elliptic partial differential equations. For the properties and applications of classical Morrey spaces, we refer the readers to [17,18,23,36,41]. Mizuhara [35] introduced generalized Morrey spaces.…”

Section: Introduction and Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Akbulut

Hasanov

2016

Open Mathematics

View full text Add to dashboard Cite

Abstract:In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels T A 1 ;A 2 ;:::;A k ;˛, which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces M p;' .w/. We find the sufficient conditions on the pair .' 1 ; ' 2 / with w 2 A p;q which ensures the boundedness of the operators T ;˛a re given in terms of Zygmund-type integral inequalities on .' 1 ; ' 2 / and w, which do not assume any assumption on monotonicity of ' 1 .x; r/; ' 2 .x; r/ in r.

show abstract

Section: Introduction and Resultsmentioning

confidence: 99%

“…Multilinear operators appear also as technical tools in the study of linear singular integral (through the method of rotations), the analysis of nonlinear operators (through power series and similar expansions), and the resolution of many linear and nonlinear partial differential equations [4,5,[15][16][17]41].…”

Section: Introduction and Resultsmentioning

confidence: 99%

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Akbulut

Hasanov

2016

Open Mathematics

View full text Add to dashboard Cite

show abstract

“…In 2004, Palagachev and Softova [8] gave the boundedness of commutator of parabolic singular integral with variable kernel on the Morrey space and gave some applications of the commutators in studying parabolic PDE.…”

Section: M(b Q(x R)) ϕ(R) < ∞mentioning

confidence: 99%

A charaterization of commutators for parabolic singular integrals

Chen¹,

Ding²

2011

MATH. SCAND.

View full text Add to dashboard Cite

In this paper, the authors give a characterization of the L p -boundedness of the commutators for the parabolic singular integrals. More precisely, the authors prove that if, where the kernel function has no any smoothness on the unit sphere S n−1 . Conversely, if assuming on a slight smoothness on S n−1 , then the boundedness ofThe results in this paper improve essentially and extend some known conclusions.

show abstract

“…See [5] and [7] and the references contained there. For applications to partial equations, see [6]. Note that when…”

Section: Preliminariesmentioning

confidence: 99%

Wolff’s inequality in multi-parameter Morrey spaces

Sjödin

2011

Math. Z.

View full text Add to dashboard Cite

show abstract

Singular Integral Operators, Morrey Spaces and Fine Regularity of Solutions to PDE's

Cited by 87 publications

References 21 publications

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

A charaterization of commutators for parabolic singular integrals

Wolff’s inequality in multi-parameter Morrey spaces

Contact Info

Product

Resources

About