Dashan Fan, Shuichi Sato (2004)
Studia Mathematica
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We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
C. Sadosky (1966)
Studia Mathematica
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Xi Chen (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
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An improved multiple Cotlar inequality is obtained. From this result, weighted norm inequalities for the maximal operator of a multilinear singular integral including weak and strong estimates are deduced under the multiple weights constructed recently.
Rafeiro, Humberto, Samko, Stefan (2007)
Fractional Calculus and Applied Analysis
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2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30 We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ =...
David E. Edmunds, Bohumír Opic
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We derive conditions, which are both necessary and sufficient, for the boundedness of (power-logarithmic) fractional maximal operators between classical and weak-type Lorentz spaces.
David Cruz-Uribe (2001)
Commentationes Mathematicae Universitatis Carolinae
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We give a new and simpler proof of a two-weight, weak inequality for fractional integrals first proved by Cruz-Uribe and Pérez [4].
Ding, Yong (2005)
International Journal of Mathematics and Mathematical Sciences
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Emile F. Doungmo Goufo, Morgan Kamga Pene, Jeanine N. Mwambakana (2015)
Open Mathematics
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We provide a mathematical analysis of a break-up model with the newly developed Caputo-Fabrizio fractional order derivative with no singular kernel, modeling rock fracture in the ecosystem. Recall that rock fractures play an important role in ecological and geological events, such as groundwater contamination, earthquakes and volcanic eruptions. Hence, in the theory of rock division, especially in eco-geology, open problems like phenomenon of shattering, which remains partially unexplained...
W. B. Jurkat, G. Sampson (1981)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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D. Cruz-Uribe, A. Fiorenza (2003)
Publicacions Matemàtiques
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Atanas Stefanov (2001)
Studia Mathematica
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We prove weak type (1,1) estimates for a special class of Calderón-Zygmund homogeneous kernels represented as l¹ sums of "equidistributed" H¹ atoms on 𝕊¹.
A. Eduardo Gatto, Carlos Segovia, Stephen Vági (1996)
Revista Matemática Iberoamericana
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In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before. We show that these operators act on Lipschitz spaces as in the classical...