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Generalized Riemann-Liouville Fractional Operators Associated with a Generalization of the Prabhakar Integral Operator
(Natural Sciences Publishing, 2016-04)
The paper introduces a new integral operator which generalizes the Prabhakar integral operator. The boundedness on the space of continuous functions and on the space of Lebesgue integrable functions on an interval is ...
On the composition of the integral and derivative operators of functional order
(Universitatis Carolinae, 2003-03)
In this work we show that the composition of the integral and derivative operators of order phi, T_phi = D_phi◦I_phi, is a singular integral operator.This result in addition with the results obtained in [HV2] of boundedness ...
Weighted inequalities for fractional integral operators with kernel satisfying Hörmander type conditions
(Element, 2011-10)
In this paper we study inequalities with weights for fractional operators Tαgiven by convolution with a kernel Kαwhich is supposed to satisfy some size condition and a fractional Hörmander type condition. As it is done for ...
Boundedness of the fractional maximal operator on variable exponent Lebesgue spaces: a short proof
(Unión Matemática Argentina, 2012-09)
We give a simple proof of the boundedness of the fractional<br />maximal operator providing in this way an alternative approach to<br />the one given by C. Capone, D. Cruz Uribe and A. Fiorenza in cite{CCUF}.
A Hölder infinity Laplacian obtained as limit of Orlicz fractional Laplacians
(Springer, 2022-05)
This paper concerns the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators ...
Certain fractional type operators with hörmander conditions
(Suomalainen Tiedeakatemia, 2018-09)
In this paper we study fractional type operators with more than one kernel, defined
by Tα,mf(x) = ˆRn k1(x − A1y)k2(x − A2y). . . km(x − Amy)f(y) dy, where, for 1 ≤ i ≤ m, each ki satisfies a fractional size condition and ...
Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators
(Academic Press Inc Elsevier Science, 2010-07)
In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain ...
Weighted inequalities for fractional type operators with some homogeneous kernels
(Springer Heidelberg, 2013-03)
In this paper, we study integral operators of the form, where Ai are certain invertible matrices, αi > 0, 1 ≤ i ≤ m, α1 + ... + αm = n - α, 0 ≤ α < n. For, we obtain the Lp(ℝn, wp) - Lq(ℝn,wq) boundedness for weights w in ...
Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces
(Czech Academy of Sciences, 2018-03)
Let μ be a nonnegative Borel measure on Rd satisfying that μ(Q) ⩽ l(Q)n for every cube Q ⊂ Rn, where l(Q) is the side length of the cube Q and 0 < n ⩽ d. We study the class of pairs of weights related to the boundedness ...
Decay rates for second-order linear evolution problems with fractional laplacian operators
(Universidade Federal de Santa Maria, 2021)