diff --git a/src/ShiftedProximalOperators.jl b/src/ShiftedProximalOperators.jl
index b21055a..d047b86 100644
--- a/src/ShiftedProximalOperators.jl
+++ b/src/ShiftedProximalOperators.jl
@@ -31,6 +31,9 @@ include("Rank.jl")
 include("cappedl1.jl")
 include("Nuclearnorm.jl")
 
+include("null.jl")
+include("shiftedNullBox.jl")
+
 include("shiftedCompositeNormL2.jl")
 include("shiftedNormL0.jl")
 include("shiftedNormL0Box.jl")
@@ -98,6 +101,7 @@ end
 set_radius!(ψ::ShiftedNormL0Box, Δ::R) where {R <: Real} = set_bounds!(ψ, -Δ, Δ)
 set_radius!(ψ::ShiftedNormL1Box, Δ::R) where {R <: Real} = set_bounds!(ψ, -Δ, Δ)
 set_radius!(ψ::ShiftedRootNormLhalfBox, Δ::R) where {R <: Real} = set_bounds!(ψ, -Δ, Δ)
+set_radius!(ψ::ShiftedNullRegularizerBox, Δ::R) where {R <: Real} = set_bounds!(ψ, -Δ, Δ)
 
 """
     set_bounds!(ψ, l, u)
diff --git a/src/null.jl b/src/null.jl
new file mode 100644
index 0000000..3f95dfa
--- /dev/null
+++ b/src/null.jl
@@ -0,0 +1,66 @@
+# Null regularizer
+export NullRegularizer
+
+@doc raw"""
+    NullRegularizer(::Type{T}) where {T <: Real}
+    NullRegularizer(lambda::T) where {T <: Real}
+
+
+Returns the null regularizer, i.e., the function that is identically zero.
+```math
+h(x) = 0
+```
+
+### Arguments
+- `T`: The type of zero that is expected to be returned by the regularizer.
+
+In the second constructor, the type of lambda is used to infer the type of zero that is expected to be returned by the regularizer. The value of lambda is ignored.
+"""
+struct NullRegularizer{T <: Real} <: ShiftedProximableFunction end
+
+NullRegularizer(lambda::T) where {T <: Real} = NullRegularizer{T}()
+NullRegularizer(::Type{T}) where {T <: Real} = NullRegularizer{T}()
+
+shifted(h::NullRegularizer{T}, xk::AbstractVector{T}) where {T <: Real} =
+  NullRegularizer(T)
+
+function shift!(h::NullRegularizer{T}, xk::AbstractVector{T}) where {T <: Real}
+  return h
+end
+
+function (h::NullRegularizer{T})(y) where {T <: Real}
+  return zero(T)
+end
+
+fun_name(h::NullRegularizer{T}) where {T <: Real} = "null regularizer"
+fun_expr(h::NullRegularizer{T}) where {T <: Real} = "t ↦ 0"
+fun_params(h::NullRegularizer{T}) where {T <: Real} = ""
+
+function Base.show(io::IO, h::NullRegularizer{T}) where {T <: Real}
+  println(io, "description : ", fun_name(h))
+  println(io, "expression  : ", fun_expr(h))
+  println(io, "parameters  : ", fun_params(h))
+end
+
+function prox!(
+  y::AbstractVector{T},
+  h::NullRegularizer{T},
+  q::AbstractVector{T},
+  ν::T
+) where {T <: Real}
+  @assert ν > zero(T)
+  y .= q
+  return y
+end
+
+function iprox!(
+  y::AbstractVector{T},
+  h::NullRegularizer{T},
+  g::AbstractVector{T},
+  d::AbstractVector{T},
+) where {T <: Real}
+  @inbounds for i ∈ eachindex(y)
+    @assert d[i] > 0
+    y[i] = - g[i] / d[i]
+  end
+end
\ No newline at end of file
diff --git a/src/shiftedNullBox.jl b/src/shiftedNullBox.jl
new file mode 100644
index 0000000..83d757f
--- /dev/null
+++ b/src/shiftedNullBox.jl
@@ -0,0 +1,111 @@
+# Null box regularizer
+export ShiftedNullRegularizerBox
+
+@doc raw"""
+    ShiftedNullRegularizerBox(h, sj, shifted_twice, l, u)
+
+Returns the shifted box null regularizer, i.e., the function that is identically zero on a box and +∞ outside of it.
+```math
+ψ(x) = h(xk + sj + x) + \chi(sj + x | [l, u])
+```
+where `h` is identically zero, `xk`represents a shift, `sj` is an additional shift that is applied to the indicator 
+function as well and `[l, u]` is the box that defines the domain of the function.
+
+### Arguments
+- `h`: The unshifted null regularizer (see `NullRegularizer`).
+- `sj`: The shift of the indicator function.
+- `shifted_twice`: A boolean indicating whether `sj` is updated or not on shifts, true means that `sj` is updated, false means that `xk` is updated.
+- `l`: The lower bound of the box.
+- `u`: The upper bound of the box.
+"""
+mutable struct ShiftedNullRegularizerBox{T <: Real, V <: AbstractVector{T}, VT <: Union{AbstractVector{T}, T}} <: ShiftedProximableFunction 
+  h::NullRegularizer{T}
+  sj::V
+  shifted_twice::Bool
+  l::VT
+  u::VT
+
+  function ShiftedNullRegularizerBox(
+    h::NullRegularizer{T},
+    sj::V,
+    shifted_twice::Bool,
+    l::VT,
+    u::VT,
+  ) where {T <: Real, V <: AbstractVector{T}, VT <: Union{AbstractVector{T}, T}}
+    new{T, V, VT}(h, sj, shifted_twice, l, u)
+  end
+end
+
+shifted(
+  h::NullRegularizer{T},
+  xk::AbstractVector{T},
+  l,
+  u,
+  selected::AbstractArray{I} = 1:length(xk),
+) where {T <: Real, I <: Integer} = shifted(h, xk, l, u)
+shifted(
+  h::NullRegularizer{T},
+  xk::AbstractVector{T},
+  l::VT,
+  u::VT,
+) where {T <: Real, VT} = ShiftedNullRegularizerBox(h, zero(xk), false, l, u)
+shifted(
+  h::NullRegularizer{T},
+  xk::AbstractVector{T},
+  Δ::T,
+  χ::Conjugate{IndBallL1{T}},
+) where {T <: Real} = ShiftedNullRegularizerBox(h, zero(xk), false, -Δ, Δ)
+shifted(
+  ψ::ShiftedNullRegularizerBox{T, V, VT},
+  sj::AbstractVector{T},
+) where {T <: Real, V <: AbstractVector{T}, VT} = ShiftedNullRegularizerBox(ψ.h, sj, true, ψ.l, ψ.u)
+
+function shift!(ψ::ShiftedNullRegularizerBox{T, V, VT}, shift::AbstractVector{T}) where {T <: Real, V <: AbstractVector{T}, VT}
+  ψ.shifted_twice && (ψ.sj .= shift)
+end
+
+function (ψ::ShiftedNullRegularizerBox{T, V})(y) where {T <: Real, V <: AbstractVector{T}}
+  ϵ = √eps(eltype(y))
+  @inbounds for i in eachindex(y)
+    l = ψ.l isa AbstractVector ? ψ.l[i] : ψ.l
+    u = ψ.u isa AbstractVector ? ψ.u[i] : ψ.u
+    if !(l - ϵ ≤ ψ.sj[i] + y[i] ≤ u + ϵ)
+      return T(Inf)
+    end
+  end
+  return zero(T)
+end
+
+fun_name(ψ::ShiftedNullRegularizerBox{T, V}) where {T <: Real, V <: AbstractVector{T}} = "shifted null regularizer with box indicator"
+fun_expr(ψ::ShiftedNullRegularizerBox{T, V}) where {T <: Real, V <: AbstractVector{T}} = "t ↦ χ({sj + t .∈ [l,u]})"
+fun_params(ψ::ShiftedNullRegularizerBox{T, V}) where {T <: Real, V <: AbstractVector{T}} =
+  "sj = $(ψ.sj)\n" * " "^14 * "l = $(ψ.l)\n" * " "^14 * "u = $(ψ.u)"
+
+function prox!(
+  y::AbstractVector{T},
+  ψ::ShiftedNullRegularizerBox{T, V},
+  q::AbstractVector{T},
+  σ::T,
+) where {T <: Real, V <: AbstractVector{T}}
+  @assert σ > zero(T)
+  @inbounds for i ∈ eachindex(y)
+    l = ψ.l isa AbstractVector ? ψ.l[i] : ψ.l
+    u = ψ.u isa AbstractVector ? ψ.u[i] : ψ.u
+    y[i] = prox_zero(q[i], l - ψ.sj[i], u - ψ.sj[i])
+  end
+  return y
+end
+
+function iprox!(
+  y::AbstractVector{T},
+  ψ::ShiftedNullRegularizerBox{T, V},
+  g::AbstractVector{T},
+  d::AbstractVector{T},
+) where {T <: Real, V <: AbstractVector{T}}
+  @inbounds for i ∈ eachindex(y)
+    l = ψ.l isa AbstractVector ? ψ.l[i] : ψ.l
+    u = ψ.u isa AbstractVector ? ψ.u[i] : ψ.u
+    y[i] = iprox_zero(d[i], g[i], l - ψ.sj[i], u - ψ.sj[i])
+  end
+  return y
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 4855827..86fc5cd 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -7,6 +7,65 @@ using Test
 
 include("test_psvd.jl")
 
+@testset "NullRegularizer" begin
+  for T in (Float64, Float32)
+    h = NullRegularizer(T)
+    @test h(T.([1.0, 1.0])) == T(0.0)
+    y = similar(T.([1.0, 2.0]))
+    prox!(y, h, T.([3.0, 4.0]), T(1.0))
+    @test all(y .== T.([3.0, 4.0]))
+    iprox!(y, h, T.([3.0, 4.0]), T.([2.0, 4.0]))
+    @test all(y .== -T.([1.5, 1.0]))
+
+    h_shifted = shifted(h, T.([1.0, 2.0]))
+    @test h_shifted(T.([1.0, 1.0])) == T(0.0)
+    prox!(y, h_shifted, T.([3.0, 4.0]), T(1.0))
+    @test all(y .== T.([3.0, 4.0]))
+    iprox!(y, h_shifted, T.([3.0, 4.0]), T.([2.0, 4.0]))
+    @test all(y .== -T.([1.5, 1.0]))
+
+    shift!(h_shifted, T.([5.0, 6.0]))
+    @test h_shifted(T.([1.0, 1.0])) == T(0.0)
+    prox!(y, h_shifted, T.([3.0, 4.0]), T(1.0))
+    @test all(y .== T.([3.0, 4.0]))
+    iprox!(y, h_shifted, T.([3.0, 4.0]), T.([2.0, 4.0]))
+    @test all(y .== -T.([1.5, 1.0]))
+
+    h_shifted_box = shifted(h, T.([1.0, 2.0]), T.([0.0, 0.0]), T.([2.0, 3.0]))
+    @test h_shifted_box.shifted_twice == false
+    @test h_shifted_box(T.([0.0, 0.0])) == T(0.0)
+    @test h_shifted_box(T.([-1.0, 0.0])) == T(Inf)
+    @test h_shifted_box(T.([2.0, 3.0])) == T(0.0)
+    @test h_shifted_box(T.([1.0, 1.5])) == T(0.0)
+    prox!(y, h_shifted_box, T.([3.0, 4.0]), T(1.0))
+    @test all(y .== T.([2.0, 3.0]))
+    iprox!(y, h_shifted_box, T.([3.0, 4.0]), T.([2.0, 4.0]))
+    @test all(y .== T.([0.0, 0.0]))
+
+    shift!(h_shifted_box, T.([5.0, 6.0]))
+
+    @test h_shifted_box(T.([0.0, 0.0])) == T(0.0)
+    @test h_shifted_box(T.([-1.0, 0.0])) == T(Inf)
+    @test h_shifted_box(T.([2.0, 3.0])) == T(0.0)
+    @test h_shifted_box(T.([1.0, 1.5])) == T(0.0)
+    prox!(y, h_shifted_box, T.([3.0, 4.0]), T(1.0))
+    @test all(y .== T.([2.0, 3.0]))
+    iprox!(y, h_shifted_box, T.([3.0, 4.0]), T.([2.0, 4.0]))
+    @test all(y .== T.([0.0, 0.0]))
+
+    h_shifted_twice_box = shifted(h_shifted_box, T.([1.0, 2.0]))
+    @test h_shifted_twice_box.shifted_twice == true
+    @test h_shifted_twice_box(T.([0.0, 0.0])) == h_shifted_box(T.([1.0, 2.0]))
+    @test h_shifted_twice_box(T.([-1.0, 0.0])) == h_shifted_box(T.([0.0, 2.0]))
+    @test h_shifted_twice_box(T.([2.0, 3.0])) == h_shifted_box(T.([3.0, 5.0]))
+    @test h_shifted_twice_box(T.([1.0, 1.5])) == h_shifted_box(T.([2.0, 3.5]))
+    prox!(y, h_shifted_twice_box, T.([3.0, 4.0]), T(1.0))
+    @test all(y .== T.([1.0, 1.0]))
+    iprox!(y, h_shifted_twice_box, T.([3.0, 4.0]), T.([2.0, 4.0]))
+    @test all(y .== T.([-1.0, -1.0]))
+  end
+end
+
 for (op, composite_op, shifted_op) ∈
     zip((:NormL2,), (:CompositeNormL2,), (:ShiftedCompositeNormL2,))
   @testset "$shifted_op" begin
diff --git a/test/test_allocs.jl b/test/test_allocs.jl
index d2824b3..9b90d39 100644
--- a/test/test_allocs.jl
+++ b/test/test_allocs.jl
@@ -37,6 +37,17 @@ macro wrappedallocs(expr)
 end
 
 @testset "allocs" begin
+
+  for op ∈ (:NullRegularizer,)
+    h = eval(op)(Float64)
+    @test @wrappedallocs(h([0.0, 0.0])) == 0
+    h_shifted_box = shifted(h, [1.0, 2.0], [0.0, 0.0], [2.0, 3.0])
+    @test @wrappedallocs(h_shifted_box([0.0, 0.0])) == 0
+    y = zeros(Float64, 2)
+    @test @wrappedallocs(prox!(y, h_shifted_box, [3.0, 4.0], 1.0)) == 0
+    @test @wrappedallocs(iprox!(y, h_shifted_box, [3.0, 4.0], [2.0, 4.0])) == 0
+  end
+
   for (op, composite_op) ∈ ((:NormL2, :CompositeNormL2),)
     CompositeOp = eval(composite_op)
 
@@ -66,7 +77,7 @@ end
     ν = 0.1056
     @test @wrappedallocs(prox!(y, ϕ, x, ν)) == 0
   end
-  for op ∈ (:NormL0, :NormL1, :RootNormLhalf)
+  for op ∈ (:NormL0, :NormL1, :RootNormLhalf,)
     h = eval(op)(1.0)
     n = 1000
     xk = rand(n)
@@ -99,7 +110,7 @@ end
     @test allocs == 0
   end
 
-  for op ∈ (:NormL0, :NormL1)
+  for op ∈ (:NormL0, :NormL1,)
     h = eval(op)(1.0)
     n = 1000
     xk = rand(n)