Saikat Kanjilal

Essential Norms of Hardy Operators into $L^\infty$ on Irregular Supports, with Bilinear Applications

We study the Hardy operator $T_hf(x)=\int_a^x h(r)f(r) dr$ from scalar $L^1(a,c)$ into $L^\infty(S)$, where $S$ is an arbitrary measurable output set, $c=\operatorname{ess\,sup} S$, and $h$ is nonnegative and essentially bounded. We identify the essential norm, the distance to fi...

Input-Endpoint Compactness and Essential Distances for Weighted Bilinear Hardy-Steklov Operators

We study weighted bilinear Hardy-Steklov operators with finite output exponent and at least one input exponent equal to one or infinity. For continuous increasing moving windows, we prove local finite-rank approximation and identify the distances to compact and finite-rank biline...

Essential Norms of Bilinear Hardy–Steklov Operators from L¹×Lᵖ to L∞

We study weighted complex-bilinear Hardy–Steklov maps from L¹×Lᵖ, 1 ≤ p ≤ ∞, and the factor-swapped spaces to literal L∞((0,∞),dx). The moving intervals have differentiable strictly increasing boundaries with the usual endpoint limits. The local dual-exponent admissibility of the...

Essential Norms of Bilinear Hardy–Steklov Operators from L¹×Lᵖ to L∞

We study weighted complex-bilinear Hardy–Steklov maps from L¹×Lᵖ, 1 ≤ p ≤ ∞, and the factor-swapped spaces to literal L∞((0,∞),dx). The moving intervals have differentiable strictly increasing boundaries with the usual endpoint limits. The local dual-exponent admissibility of the...

Incidence Geometry and L∞ Essential Norms of Bilinear Hardy–Steklov Operators

We study weighted bilinear Hardy–Steklov operators whose moving intervals have differentiable strictly increasing endpoints, with both endpoints tending to zero and infinity at the corresponding ends of the half-line. For complex inputs in the exact sector 1 < p₁, p₂ ≤ ∞ and lite...