Construction of an optimal envelope for a cone of nonnegative functions with monotonicity properties

Bakhtigareeva, E. G.; Goldman, M. L.

doi:10.1134/s0081543816040039

Cited by 4 publications

(6 citation statements)

References 7 publications

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“…Proof 1. Recall the properties (B1) to (B4) of an IS with (quasi)norm

false| false| \cdot false| false|

(see Bakhtigareeva and Goldman 11 ): for

M_{E F}

properties

false(B 2 false)

and

false(B 3 false)

, follow from related properties of

E

, as it was shown in the proof of Theorem 3. In property

false(B 1 false)

, we have to establish a triangle inequality.…”

Section: Generalized Morrey Spacesmentioning

confidence: 90%

“…Remark Some general properties of ISs were described in Bakhtigareeva and Goldman 11 . In particular,

L M_{E F}

and

G M_{E F}

are quasi‐Banach spaces of measurable functions (Banach spaces if

E

and

F

are normed spaces).…”

Section: Generalized Morrey Spacesmentioning

confidence: 97%

“…Here, we generalize the system of axioms for Banach function spaces (BFS) and RISs given by Bennett and Sharpley. 10 First, we recall the definition of an IS X = X(R n ) with a (quasi)norm || • || (see Bakhtigareeva and Goldman 11 ). Definition 1.…”

Section: Ideal and Rearrangement Invariant Spacesmentioning

confidence: 99%

“…First, we recall the definition of an IS

X = X false(R^{n} false)

with a (quasi)norm

false| false| \cdot false| false|

(see Bakhtigareeva and Goldman 11 ).…”

Section: Ideal and Rearrangement Invariant Spacesmentioning

confidence: 99%

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Application of general approach to the theory of Morrey‐type spaces

Goldman

Bakhtigareeva

2020

Math Methods in App Sciences

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“…Proof 1. Recall the properties (B1) to (B4) of an IS with (quasi)norm

false| false| \cdot false| false|

(see Bakhtigareeva and Goldman 11 ): for

M_{E F}

properties

false(B 2 false)

and

false(B 3 false)

, follow from related properties of

E

, as it was shown in the proof of Theorem 3. In property

false(B 1 false)

, we have to establish a triangle inequality.…”

Section: Generalized Morrey Spacesmentioning

confidence: 90%

“…Remark Some general properties of ISs were described in Bakhtigareeva and Goldman 11 . In particular,

L M_{E F}

and

G M_{E F}

are quasi‐Banach spaces of measurable functions (Banach spaces if

E

and

F

are normed spaces).…”

Section: Generalized Morrey Spacesmentioning

confidence: 97%

Section: Ideal and Rearrangement Invariant Spacesmentioning

confidence: 99%

“…First, we recall the definition of an IS

X = X false(R^{n} false)

with a (quasi)norm

false| false| \cdot false| false|

(see Bakhtigareeva and Goldman 11 ).…”

Section: Ideal and Rearrangement Invariant Spacesmentioning

confidence: 99%

See 2 more Smart Citations

Application of general approach to the theory of Morrey‐type spaces

Goldman

Bakhtigareeva

2020

Math Methods in App Sciences

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show abstract

“…When we study the relations between different intermediate spaces, we have to invoke the results on the estimates on the cone Ω (0) (1) .…”

Section: Interpolation Theorymentioning

confidence: 99%

Calculations of the norms for monotone operators on the cones of functions with monotonicity properties

Bakhtigareeva¹,

Goldman²

2021

Preprint

Self Cite

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The paper is devoted to the problem of exact calculation of the norms in ideal spaces for monotone operators on the cones of functions with monotonicity properties. We implement a general approach to this problem that covers many concrete variants of monotone operators in ideal spaces and different monotonicity conditions for functions. As applications, we calculate the norms of some integral operators on the cones, associate norms over some cones in Lebesgue spaces, the norms of the dilation operator and embedding operators on weighted Lorentz spaces with general weights. Under some more general conditions, we present order sharp estimates for Hardy-type operators on the cones.

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On Calculation of the Norm of a Monotone Operator in Ideal Spaces

Bakhtigareeva,

Goldman

2024

J Math Sci

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Construction of an optimal envelope for a cone of nonnegative functions with monotonicity properties

Cited by 4 publications

References 7 publications

Application of general approach to the theory of Morrey‐type spaces

Application of general approach to the theory of Morrey‐type spaces

Calculations of the norms for monotone operators on the cones of functions with monotonicity properties

On Calculation of the Norm of a Monotone Operator in Ideal Spaces

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