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A new class of general refined Hardy-type inequalities with kernels

Aleksandra Čižmešija ; Department of Mathematics, University of Zagreb, Bijeniˇcka cesta 30, 10000 Zagreb, Croatia
Kristina Krulić ; Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovi´ca 28a, 10000 Zagreb, Croatia
Josip Pečarić ; Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovi´ca 28a, 10000 Zagreb, Croatia

Puni tekst: engleski, pdf (483 KB) str. 53-80 preuzimanja: 415* citiraj
APA 6th Edition
Čižmešija, A., Krulić, K. i Pečarić, J. (2013). A new class of general refined Hardy-type inequalities with kernels. Rad Hrvatske akademije znanosti i umjetnosti, (515=17), 53-80. Preuzeto s https://hrcak.srce.hr/104406
MLA 8th Edition
Čižmešija, Aleksandra, et al. "A new class of general refined Hardy-type inequalities with kernels." Rad Hrvatske akademije znanosti i umjetnosti, vol. , br. 515=17, 2013, str. 53-80. https://hrcak.srce.hr/104406. Citirano 10.08.2020.
Chicago 17th Edition
Čižmešija, Aleksandra, Kristina Krulić i Josip Pečarić. "A new class of general refined Hardy-type inequalities with kernels." Rad Hrvatske akademije znanosti i umjetnosti , br. 515=17 (2013): 53-80. https://hrcak.srce.hr/104406
Harvard
Čižmešija, A., Krulić, K., i Pečarić, J. (2013). 'A new class of general refined Hardy-type inequalities with kernels', Rad Hrvatske akademije znanosti i umjetnosti, (515=17), str. 53-80. Preuzeto s: https://hrcak.srce.hr/104406 (Datum pristupa: 10.08.2020.)
Vancouver
Čižmešija A, Krulić K, Pečarić J. A new class of general refined Hardy-type inequalities with kernels. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2013 [pristupljeno 10.08.2020.];(515=17):53-80. Dostupno na: https://hrcak.srce.hr/104406
IEEE
A. Čižmešija, K. Krulić i J. Pečarić, "A new class of general refined Hardy-type inequalities with kernels", Rad Hrvatske akademije znanosti i umjetnosti, vol., br. 515=17, str. 53-80, 2013. [Online]. Dostupno na: https://hrcak.srce.hr/104406. [Citirano: 10.08.2020.]

Sažetak
Let μ1 and μ2 be positive sigma-finite measures on Omega1 and Omega2
respectively, k : Omega1 × Omega2 --> R be a non-negative function, and
K(x) = int_Omega2 k(x, y) dμ2(y), x in Omega1.
We state and prove a new class of refined general Hardy-type inequalities related to the weighted Lebesgue spaces Lp and Lq, where 0 < p <= q < infinity or −infinity < q <= p < 0, convex functions and the integral operators Ak of the form
Ak f(x) =1/K(x) int_Omega2 k(x, y)f(y) dμ2(y).
We also provide a class of new sufficient conditions for a weighted modular
inequality involving operator Ak to hold. As special cases of our
results, we obtain refinements of the classical one-dimensional Hardy’s,
Polya–Knopp’s and Hardy–Hilbert’s inequality and of related dual inequalities,
as well as a generalization and refinement of the classical
Godunova’s inequality. Finally, we show that our results may be seen
as generalizations of some recent results related to Riemann-Liouville’s
and Weyl’s operator.

Ključne riječi
Hardy’s inequality; Hardy-Hilbert’s inequality; weights; power weights; convex functions; Hardy’s operator; kernel

Projekti
MZOS / ZP / 058-1170889-1050 - Ocjene za funkcionale na prostorima funkcija
MZOS / ZP / 117-1170889-0888 - Generalne nejednakosti i primjene

Hrčak ID: 104406

URI
https://hrcak.srce.hr/104406

Posjeta: 534 *