Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels
Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels
Genebashvili, I.; Gogatishvili, A.; Kokilashvili, V.
1994-02-01 00:00:00
Necessary and sufficient conditions are derived in order that an inequality of the form be fulfilled for some positive c independent of ॕ and a ν -measurable nonnegative function ƒ : X → R 1 , where k : X × X × 0, ∞) → R 1 is a nonnegative measurable kernel, ( X, d, μ ) is a homogeneous type space, ०॑ and २ are quasiconvex functions, २ ∈ Δ 2 , and t – α θ ( t ) is a decreasing function for some α , 0 < α < 1. A similar problem was solved in Lorentz spaces with weights.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngGeorgian Mathematical Journalde Gruyterhttp://www.deepdyve.com/lp/de-gruyter/criteria-of-general-weak-type-inequalities-for-integral-transforms-owB67rrTXS
Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels
Necessary and sufficient conditions are derived in order that an inequality of the form be fulfilled for some positive c independent of ॕ and a ν -measurable nonnegative function ƒ : X → R 1 , where k : X × X × 0, ∞) → R 1 is a nonnegative measurable kernel, ( X, d, μ ) is a homogeneous type space, ०॑ and २ are quasiconvex functions, २ ∈ Δ 2 , and t – α θ ( t ) is a decreasing function for some α , 0 < α < 1. A similar problem was solved in Lorentz spaces with weights.
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