Wyniki wyszukiwania

1

First and second order Opial inequalities

100%

Bloom S.

Studia Mathematica

|

1997

|

tom 126

|

nr 1

27-50

EN

Let $T_γ f(x) = ʃ_0^x k(x,y)^γ f(y)dy$, where k is a nonnegative kernel increasing in x, decreasing in y, and satisfying a triangle inequality. An nth-order Opial inequality has the form $ʃ_0^∞ (∏_{i=1}^n |T_{γ_i}f(x)|^{q_i}|) |f(x)|^{q_0} w(x)dx ≤ C(ʃ_0^∞ |f(x)|^p v(x)dx)^{(q_0+…+q_n)/p}$. Such inequalities can always be simplified to nth-order reduced inequalities, where the exponent $q_0 = 0$. When n = 1, the reduced inequality is a standard weighted norm inequality, and characterizing the weights is easy. We also find necessary and sufficient conditions on the weights for second-order reduced Opial inequalities to hold.

2

Weighted $L_{Φ}$ integral inequalities for operators of Hardy type

63%

Bloom S., Kerman R.

Studia Mathematica

|

1994

|

tom 110

|

nr 1

35-52

EN

Necessary and sufficient conditions are given on the weights t, u, v, and w, in order for $Φ_2^{-1} (ʃΦ_2(w(x)|Tf(x)|)t(x)dx) ≤ Φ_{1}^{-1}(ʃΦ_{1}(Cu(x)|f(x)|)v(x)dx)$ to hold when $Φ_1$ and $Φ_2$ are N-functions with $Φ_2∘Φ_{1}^{-1}$ convex, and T is the Hardy operator or a generalized Hardy operator. Weak-type characterizations are given for monotone operators and the connection between weak-type and strong-type inequalities is explored.

3

An interpolation theorem with $A_{p}$-weighted $L^{p}$ spaces

38%

Bloom S.

Studia Mathematica

|

1990

|

tom 96

|

nr 1

11-15

4

Sharp weights and BMO-preserving homeomorphisms

32%

Bloom S.

Studia Mathematica

|

1990

|

tom 96

|

nr 1

1-10

Ograniczanie wyników

4 Studia Mathematica

4 Bloom S.

1 Kerman R.

1 1997

1 1994

2 1990

First and second order Opial inequalities

Weighted $L_{Φ}$ integral inequalities for operators of Hardy type

An interpolation theorem with $A_{p}$-weighted $L^{p}$ spaces

Sharp weights and BMO-preserving homeomorphisms