scholarly journals Necessary and sufficient conditions for the boundedness of the maximal operator from Lebesgue spaces to Morrey-type spaces

2014 ◽  
pp. 401-418
Author(s):  
Victor Burenkov ◽  
M. L. Goldman
Keyword(s):  
Maximal Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lebesgue Spaces ◽  
Type Spaces ◽  
Necessary And Sufficient

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

scholarly journals Potential Operators on Cones of Nonincreasing Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Alexander Meskhi ◽  
Ghulam Murtaza
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Product Type ◽  
Necessary And Sufficient Conditions ◽  
Lebesgue Spaces ◽  
Potential Operators ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient

Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators(Iαf)(x)=∫0∞(f(t)/|x−t|1−α)dtand(ℐα1,α2f)(x,y)=∫0∞∫0∞(f(t,τ)/|x−t|1−α1|y−τ|1−α2)dtdτon the cone of nonincreasing functions are derived. In the case ofℐα1,α2, we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between 1 and ∞.

scholarly journals On bilinear weighted inequalities with Volterra integral operators

2019 ◽  
Vol 486 (4) ◽  
pp. 416-420
Author(s):  
V. D. Stepanov ◽  
G. E. Shambilova
Keyword(s):  
Sufficient Conditions ◽  
Integral Operators ◽  
Necessary And Sufficient Conditions ◽  
Weighted Inequalities ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Necessary And Sufficient

Necessary and sufficient conditions on the boundedness in weighted Lebesgue spaces on the semiaxis for bilinear inequalities with Volterra integral operators are given.

scholarly journals Summability of a Tchebysheff system of functions

2010 ◽  
Vol 8 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Z. T. Abdikalikova ◽  
A. A. Kalybay
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Independent Interest ◽  
Lebesgue Spaces ◽  
Necessary And Sufficient

We consider a special type of Tchebysheff systems of functions{ui(⋅)}in=0and{Vi(⋅)}in=0defined on the intervals (0, 1] and [1,+∞), respectively, such thatui(t)=tα0∫t1t1α1∫t11t2α2…∫ti−11tiαidtidti−1…dt1andui(t)=tβ0∫1tt1β1∫1t1t2β2…∫1ti−1tiβidtidti−1…dt1. We find necessary and sufficient conditions under which functions from the investigated systems belong to the corresponding Lebesgue spacesLp(0, 1) andLp(1,+∞). In order to prove the main results we obtain lower and upper estimates of these functions that are of independent interest.

scholarly journals Measure convergent sequences in Lebesgue spaces and Fatou's lemma

1996 ◽  
Vol 54 (2) ◽  
pp. 197-202 ◽  
Author(s):  
Heinz-Albrecht Klei
Keyword(s):  
Integrable Function ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Uniform Integrability ◽  
Lebesgue Spaces ◽  
Integrable Functions ◽  
Fatou’S Lemma ◽  
Necessary And Sufficient ◽  
Fatou's Lemma ◽  
Convergent Sequences

Let (fn) be a sequence of positive P-integrable functions such that (∫ fndP)n converges. We prove that (fn) converges in measure to if and only if equality holds in the generalised Fatou's lemma. Let f∞ be an integrable function such that (∥fn − f∞∥1)n converges. We present in terms of the modulus of uniform integrability of (fn) necessary and sufficient conditions for (fn) to converge in measure to f∞.

Riesz potential in the local Morrey–Lorentz spaces and some applications

2020 ◽  
Vol 27 (4) ◽  
pp. 557-567
Author(s):  
Vagif S. Guliyev ◽  
Abdulhamit Kucukaslan ◽  
Canay Aykol ◽  
Ayhan Serbetci
Keyword(s):  
Maximal Operator ◽  
Riesz Potential ◽  
Sufficient Conditions ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Analytic Semigroups ◽  
Fractional Powers ◽  
Marcinkiewicz Operator ◽  
Fractional Maximal Operator ◽  
Necessary And Sufficient

AbstractIn this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential {I_{\alpha}} in the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}. This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}.

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