| 31. |
- Maligranda, Lech, et al.
(författare)
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On n-th James and Khintchine constants of Banach spaces
- 2008
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 11:1, s. 1-22
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Tidskriftsartikel (refereegranskat)abstract
- For any Banach space X the n-th James constants J(n)(X) and the n-th Khintchine constants K-p,q(n)(X) are investigated and discussed. Some new properties of these constants are presented. The main result is an estimate of the n-th Khintchine constants K-p,q(n)(X) by the n-th James constants Jn (X). In the case of n = 2 and p = q = 2 this estimate is even stronger and improvs an earlier estimate proved by Kato-Maligranda-Takahashi
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| 32. |
- Maligranda, Lech, et al.
(författare)
-
Real and complex operator norms between quasi-banach Lp -L q spaces
- 2011
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 14:2, s. 247-270
-
Tidskriftsartikel (refereegranskat)abstract
- Relations between the norms of an operator and its complexification as a mapping from Lp to Lq has been recognized as a serious problem in analysis after the publication of Marcel Riesz's work on convexity and bilinear forms in 1926. We summarize here what it is known about these relations in the case of normed Legesgue spaces and investigate the quasinormed case, i. e. we consider all 0 < p,q ≤ 8 . In particular, in the lower triangle, that is, for 0< p≤q≤∞ these norms are the same. In the upper triangle and the normed case, that is, when 1 ≤ q < p ≤ ∞ the norm of the complexification of a real operator is obviously not bigger than 2 times its real norm. In 1977 Krivine proved that the constant 2 can be replaced by √2 . On the other hand, it was suspected that in the case of quasi-normed Lebesgue spaces (0 < q < p ≤ ∞ ) the corresponding constant could be arbitrarily large, but as we will see this is not the case. More precisely, we prove that this constant for quasi-normed Lebesgue spaces is between 1 and 2. Some additional properties and estimates of this constant with some results about the relation between complex and real norms of operators, including those between two-dimensional Orlicz spaces are presented in the first four chapters. Finally, in Chapter 5, we use the results on the estimates of the norms in the proof of the real Riesz-Thorin interpolation theorem valid in the first quadrant
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| 33. |
- Maligranda, Lech
(författare)
-
Why Hölder's inequality should be called Rogers' inequality
- 1998
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 1:1, s. 69-83
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Tidskriftsartikel (refereegranskat)abstract
- This reviewer remembers Leopold Fejér (1880-1959) saying (in Hungarian) that ``the history of mathematics serves to prove that nobody discovered anything: there was always somebody who had known it before'' (quoted in English in the present paper). The author argues convincingly about who had priority to the inequalities of Hölder (Rogers), Cauchy (Lagrange), Jensen (Hölder) and others. Also equivalences and relations between different forms and different inequalities and several proofs are offered. The paper concludes with biographical sketches of Leonard James Rogers and Otto Ludwig Hölder.
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| 34. |
- Mamedov, Farman, et al.
(författare)
-
A new fractional order poincare's inequality with weights
- 2020
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Ingår i: Mathematical Inequalities & Applications. - : ELEMENT. - 1331-4343 .- 1848-9966. ; 23:2, s. 611-624
-
Tidskriftsartikel (refereegranskat)abstract
- We derive a new Sawyer's type sufficient condition for the fractional order Poincare inequality with weights (integral(Omega) vertical bar f(x) - (f) over bar (v,Omega)vertical bar(q) upsilon(x)dx)1/q <= C (integral integral(Omega x Omega) vertical bar f(x) - f(y)vertical bar(p) omega(x,y)dxdy)1/p to hold in a non-regular domain Omega subset of R-n of finite volume, where omega(x,y) = vertical bar x - y vertical bar(-n-alpha P) omega(0)(x,y), 0 < alpha < 1, q >= p > 1, f is an element of C(Omega), and v(.), omega(.,.) are positive measurable functions such that omega(1-p')(x,.)v(p')(.) is an element of L(Omega) a.e. x is an element of Omega and (f) over bar (v,Omega) = 1/upsilon(Omega) integral(Omega) fvdx.
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| 35. |
- Moslehianand, M.S., et al.
(författare)
-
Reverse Cauchy-Schwarz inequalities for positive C*-valued sesquilinear forms
- 2009
-
Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 12:4, s. 701-709
-
Tidskriftsartikel (refereegranskat)abstract
- We prove two new reverse Cauchy-Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C*-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy-Schwarz inequality due to G. Polya and G. Szego
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| 36. |
- Nagy, Károly, et al.
(författare)
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Strong convergence theorem for Walsh-Marcinkiewicz means
- 2016
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 19:1, s. 185-195
-
Tidskriftsartikel (refereegranskat)abstract
- It is known that the maximal operator ofWalsh-Marcinkiewicz means is bounded from the dyadic martingale Hardy space Hp to the space Lp for p > 2/3 and the condition p > 2/3 is essential. In the case p = 2/3 the boundedness of the maximal operator does not hold. This means that the investigation of the maximal operator at the endpoint case p = 2/3 plays an important role. The main aim of this paper is to prove a strong convergence theorem for the Walsh-Marcinkiewicz means on the Hardy space H2/3.
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| 37. |
- Nikolova, Ludmila, et al.
(författare)
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Weighted Hardy and Pólya-Knopp inequalities with variable limits
- 2007
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:3, s. 547-557
-
Tidskriftsartikel (refereegranskat)abstract
- A new scale of characterizations for the weighted Hardy inequality with variable limits is proved for the case 1 < p ≤ q < ∞. A corresponding scale of characterizations for the (limit) weighted Pólya-Knopp inequality is also derived and discussed.
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| 38. |
- Oinarov, Ryskul, et al.
(författare)
-
OSCILLATORY AND SPECTRAL PROPERTIES OF A CLASS OF FOURTH-ORDER DIFFERENTIAL OPERATORS VIA A NEW HARDY-TYPE INEQUALITY
- 2024
-
Ingår i: Mathematical Inequalities & Applications. - : ELEMENT. - 1331-4343 .- 1848-9966. ; 27:1, s. 63-83
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. These properties are established by first proving a new second-order Hardy-type inequality, where the weights are the coefficients of the equation and the operator. This new inequality, in its turn, is established for functions satisfying certain boundary conditions that depend on the boundary behavior of one of its weights at infinity and at zero.
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| 39. |
- Oinarov, R., et al.
(författare)
-
Weighted inequalities for a class of matrix operators : the case of p≤q
- 2009
-
Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 12:4, s. 891-903
-
Tidskriftsartikel (refereegranskat)abstract
- We prove a new discrete Hardy-type inequality ||A/||q,u ≤ C||f||p,v, where the matrix operator A is defined by (Af) i:= Σj=1i ai,jfj, ai,j ≥ 0. Moreover, we study die problem of compactness of the operator A, and die dual result is stated
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| 40. |
- Omarbayeva, B.K., et al.
(författare)
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Weighted iterated discrete Hardy-type inequalities
- 2020
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Ingår i: Mathematical Inequalities & Applications. - : Element D.O.O.. - 1331-4343 .- 1848-9966. ; 23:3, s. 943-959
-
Tidskriftsartikel (refereegranskat)abstract
- Necessary and sufficient conditions on functions u and omega are established ensuring boundedness of a discrete Hardy-type operator from a weighted sequence space l(p,u) to a weighted sequence space for a wide range of the numerical parameters p,u and theta.
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