Spaces with asymmetric norm - Open Access .click

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Multidimensional inequalities between distinct metrics in spaces with an asymmetric norm

Sbornik: Mathematics, 1998
For \(T^d\) the \(d\)-dimensional torus, \(L_{p,q}(T^d)\) is the space of functions \(f\) on \(T^d\) with \(f^+\in L_p(T^d)\), \(f^-\in L_q(T^d)\) and the norm \(\| f\|_{p,q}=\| f^+\|_p +\| f^-\|_q\). The trigonometric polynomial \(T_n\) of degree \(n_j\) in \(x_j\) satisfies the Jackson-Nikolskij type inequality \[ \| T_n\|_{q_1,q_2}\leq C_ ...
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Fractional derivatives and inequalities for trigonometric polynomials in spaces with asymmetric norms

Izvestiya: Mathematics, 1998
For \(p_1, p_2\in [1, \infty] \) the asymmetric norm of a real-valued measurable function \(f\) on \([-\pi, \pi]\) is defined by \(\|f \|_{p_1,p_2}=\|f^{+}\|_{p_1} + \|f^{-}\|_{p_2}\), where \(f^{+}(t)=\max \{0; f(t)\}\) and \(f^{-}(t)=\max \{0; -f(t)\}\).
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THE EXISTENCE OF EXTREME POINTS OF COMPACT CONVEX SETS IN ASYMMETRIC CONE NORMED SPACES

Journal of Mathematical Analysis
Optimization has been one of the most popular applications in real-world problems from the past into the present. The concept of extreme points plays a vital role in optimization, and the existence of extreme points of compact convex subsets of a locally convex (Hausdorff) vector space can be obtained from the Krein-Milman theorem.
WASIN SUPAKUL, WUTIPHOL SINTUNAVARAT
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Contractive inequalities for mixed norm spaces and the Beta function

Journal of Mathematical Analysis and Applications, 2022
Dragan Vukotić, Adrian Llinares
exaly

Mixed-Norm Amalgam Spaces and Their Predual

Symmetry, 2022
Jiang Zhou
exaly

Separation axioms and covering dimension of asymmetric normed spaces

Quaestiones Mathematicae, 2020
Natalia Jonard Perez
exaly

Mixed norm spaces and rearrangement invariant estimates

Journal of Mathematical Analysis and Applications, 2014
Nadia Clavero, Javier Soria
exaly

A characterization of the inclusions between mixed norm spaces

Journal of Mathematical Analysis and Applications, 2015
Irina Arévalo
exaly

Norm of the Hilbert matrix on Bergman and Hardy spaces and a theorem of Nehari type

Journal of Functional Analysis, 2008
Dragan Vukotić
exaly